Geometry becomes much more interesting when students start understanding how circles follow fixed mathematical properties and relationships, and that is exactly what students learn in the Circles chapter of Class 10 Maths. This chapter mainly focuses on tangents, points of contact, radius relationships, and theorem-based geometry concepts that help students improve logical reasoning and visual understanding for CBSE board exams. Practicing Circles MCQs Class 10 regularly helps students strengthen theorem application, diagram interpretation, and geometry-solving skills for competency-based objective questions. The latest CBSE pattern now focuses more on conceptual reasoning and practical theorem understanding instead of direct memorization, which makes regular MCQ practice extremely important for improving confidence and accuracy. Students preparing for examinations can also explore MCQs, Class 10 MCQs, CBSE Board, and MCQs Class 10 Maths for chapter-wise objective practice based on the latest exam pattern and concept-focused preparation strategy.
Why Circles is an Important Chapter in Class 10 Maths
The Circles chapter is considered highly important because it teaches students how geometry relationships work through tangents, radii, and theorem-based reasoning.
Instead of lengthy calculations, this chapter mainly focuses on:
understanding geometric properties,
observing diagrams carefully,
and applying circle theorems logically.
This chapter is important because:
Questions are regularly asked in CBSE board exams
Geometry visualization skills improve significantly
Theorem application becomes stronger
Diagram interpretation accuracy improves
Competency-based questions are increasing
Logical reasoning develops naturally
Students understand practical geometric relationships better
Students who understand circle properties properly usually solve geometry questions more confidently later.
Important Concepts Students Learn in Circles
Before solving Circles MCQs Class 10 with Answers, students should revise all important concepts carefully because many objective questions are directly theorem and diagram based.
Important topics covered in this chapter include:
- Tangent to a circle
- Point of contact
- Radius and tangent relationship
- External point
- Equal tangents theorem
- Circle properties
- Tangent length relationships
- Perpendicular radius concept
- Geometry theorem application
- Circle-based diagram analysis
A proper understanding of these concepts helps students solve board-level geometry MCQs much more accurately.
Circles MCQs with Answers
Practice important and exam-oriented Circles MCQs Class 10 designed according to the latest CBSE pattern and competency-based learning approach. These objective questions help students improve theorem understanding, geometric reasoning, tangent concepts, and board exam preparation skills effectively.
Q. From an external point P, a tangent PT is drawn to a circle with center O. If OP = 15 cm and radius = 9 cm, find the length of the tangent.
A) 10 cm
B) 12 cm
C) 9 cm
D) 6 cm
Answer: B
Explanation:
In right triangle OPT,
PT = sqrt(OP^2 - OT^2)
= sqrt(15^2 - 9^2)
= sqrt(225 - 81)
= sqrt(144) = 12 cm.
Q. The angle between two tangents drawn from an external point to a circle is 80 degree. Find the angle subtended by the points of contact at the center.
A) 80 degree
B) 90 degree
C) 100 degree
D) 120 degree
Answer: C
Explanation:
Angle between tangents + angle at center = 180 degree
Therefore, angle at center = 180 - 80 = 100 degree.
Q. The length of the tangent from a point 17 cm away from the center of a circle of radius 8 cm is:
A) 12 cm
B) 15 cm
C) 9 cm
D) 10 cm
Answer: B
Explanation:
Tangent length = sqrt(17^2 - 8^2)
= sqrt(289 - 64)
= sqrt(225) = 15 cm.
Q. A tangent to a circle is always perpendicular to the radius at the:
A) Center
B) Diameter
C) Point of contact
D) Chord
Answer: C
Explanation:
A tangent touches the circle at exactly one point and is perpendicular to the radius at that point.
Q. Two concentric circles have radii 13 cm and 5 cm. Find the length of the chord of the larger circle touching the smaller circle.
A) 20 cm
B) 24 cm
C) 18 cm
D) 10 cm
Answer: B
Explanation:
Half chord = sqrt(13^2 - 5^2)
= sqrt(169 - 25)
= sqrt(144) = 12 cm
Full chord = 2 x 12 = 24 cm.
Q. How many tangents can be drawn from a point lying inside the circle?
A) 0
B) 1
C) 2
D) Infinite
Answer: A
Explanation:
A tangent cannot be drawn from a point inside the circle because every line through the point intersects the circle at two points.
Q. The maximum number of tangents that can be drawn to a circle parallel to each other is:
A) 1
B) 2
C) 3
D) Infinite
Answer: B
Explanation:
Only two parallel tangents can exist on opposite sides of a circle.
Q. If the radius of a circle is 7 cm, then the distance between two parallel tangents is:
A) 7 cm
B) 14 cm
C) 21 cm
D) 28 cm
Answer: B
Explanation:
Distance between two parallel tangents = diameter = 2 x 7 = 14 cm.
Q. From a point P outside a circle, PA and PB are tangents. If angle APB = 50 degree, then angle AOB is:
A) 130 degree
B) 120 degree
C) 140 degree
D) 150 degree
Answer: A
Explanation:
Angle between tangents + angle at center = 180 degree
Angle AOB = 180 - 50 = 130 degree.
Q. A tangent intersects a circle at:
A) Two points
B) One point
C) Three points
D) No point
Answer: B
Explanation:
A tangent touches the circle at exactly one point.
Q. If OP = 25 cm and tangent PT = 24 cm, then radius OT is:
A) 5 cm
B) 6 cm
C) 7 cm
D) 8 cm
Answer: C
Explanation:
OT = sqrt(25^2 - 24^2)
= sqrt(625 - 576)
= sqrt(49) = 7 cm.
Q. A quadrilateral circumscribing a circle satisfies which relation?
A) Opposite angles are equal
B) Sum of opposite sides are equal
C) Adjacent sides are equal
D) Diagonals are equal
Answer: B
Explanation:
In a tangential quadrilateral, sum of one pair of opposite sides equals sum of the other pair.
Q. If two tangents drawn from an external point are equal, then they meet the circle at:
A) Equal radii
B) Equal chords
C) Equal distances from center
D) Different points of contact
Answer: D
Explanation:
Tangents from an external point touch the circle at two distinct points.
Q. If angle between two radii is 150 degree, then angle between corresponding tangents is:
A) 30 degree
B) 40 degree
C) 50 degree
D) 60 degree
Answer: A
Explanation:
Angle between tangents = 180 - 150 = 30 degree.
Q. A circle has infinite number of:
A) Diameters only
B) Tangents only
C) Chords only
D) Tangents and chords
Answer: D
Explanation:
A circle contains infinitely many points, so infinitely many tangents and chords are possible.
Q. If the tangent length from an external point is 20 cm and radius is 15 cm, find the distance of the point from the center.
A) 25 cm
B) 30 cm
C) 35 cm
D) 18 cm
Answer: A
Explanation:
Distance from center = sqrt(20^2 + 15^2)
= sqrt(400 + 225)
= sqrt(625) = 25 cm.
Q. If AB and AC are tangents from point A to a circle, then AB and AC are:
A) Parallel
B) Perpendicular
C) Equal
D) Unequal
Answer: C
Explanation:
Tangents drawn from an external point to a circle are always equal.
Q. The common point of a tangent and a circle is called:
A) Midpoint
B) Point of contact
C) Center
D) Radius point
Answer: B
Explanation:
The point where a tangent touches the circle is called the point of contact.
Q. Two circles touch externally. If their radii are 8 cm and 5 cm, then the distance between their centers is:
A) 3 cm
B) 8 cm
C) 13 cm
D) 40 cm
Answer: C
Explanation:
Distance between centers of externally touching circles = sum of radii
= 8 + 5 = 13 cm.
Q. A secant intersects a circle at:
A) One point
B) Two points
C) Three points
D) No point
Answer: B
Explanation:
A secant cuts the circle at two distinct points.
Q. The angle between a tangent and the radius at the point of contact is:
A) 45 degree
B) 60 degree
C) 90 degree
D) 180 degree
Answer: C
Explanation:
Radius is always perpendicular to tangent at the point of contact.
Q. If the radius of a circle is doubled, then its diameter becomes:
A) Half
B) Double
C) Triple
D) Four times
Answer: B
Explanation:
Diameter = 2 x radius.
Doubling the radius doubles the diameter.
Q. If OP = 10 cm and radius = 6 cm, then tangent length PT is:
A) 6 cm
B) 8 cm
C) 10 cm
D) 12 cm
Answer: B
Explanation:
PT = sqrt(10^2 - 6^2)
= sqrt(100 - 36)
= sqrt(64) = 8 cm.
Q. The center of a circle lies on the:
A) Tangent
B) Diameter
C) Radius
D) Circumference
Answer: B
Explanation:
The center always lies on every diameter of the circle.
Q. If the angle between two tangents from an external point is 110 degree, then the angle subtended at the center is:
A) 70 degree
B) 80 degree
C) 90 degree
D) 100 degree
Answer: A
Explanation:
Angle at center = 180 - 110 = 70 degree.
Q. A chord passing through the center of a circle is called:
A) Radius
B) Tangent
C) Diameter
D) Arc
Answer: C
Explanation:
A diameter is the longest chord passing through the center.
Q. If the diameter of a circle is 18 cm, then radius is:
A) 18 cm
B) 9 cm
C) 6 cm
D) 3 cm
Answer: B
Explanation:
Radius = diameter/2 = 18/2 = 9 cm.
Q. If tangents PA and PB are drawn from an external point P, then triangle APB is always:
A) Equilateral
B) Isosceles
C) Right-angled
D) Scalene
Answer: B
Explanation:
PA = PB because tangents from an external point are equal.
Q. Two circles touch internally. If their radii are 12 cm and 7 cm, then distance between centers is:
A) 5 cm
B) 19 cm
C) 7 cm
D) 12 cm
Answer: A
Explanation:
Distance between centers of internally touching circles = difference of radii
= 12 - 7 = 5 cm.
Q. The line joining the center of a circle to the point of contact of a tangent is:
A) Parallel to tangent
B) Equal to tangent
C) Perpendicular to tangent
D) Inclined at 45 degree
Answer: C
Explanation:
Radius through the point of contact is always perpendicular to the tangent.
Instructions Before Solving Circles MCQs
- Read the diagram carefully before selecting the answer because many circle questions are observation-based.
- Identify the tangent and radius properly before applying any theorem.
- Check the point of contact carefully because most theorem relationships depend on it.
- Remember that the radius and tangent always form a right angle at the point of contact.
- Use geometric reasoning step-by-step instead of making assumptions from the diagram directly.
- Practice competency-based and theorem-oriented objective questions regularly because the latest CBSE pattern focuses heavily on conceptual understanding.
- Avoid rushing through geometry diagrams because small observation mistakes can change the entire answer.
- Revise theorem statements regularly to improve confidence and solving speed.
Mistakes Students Commonly Make in Circle Questions
Many students lose marks in Circles MCQs Class 10 because of incorrect theorem application and diagram interpretation mistakes.
Some common mistakes include:
- Confusing tangent with chord
- Incorrect point of contact identification
- Forgetting perpendicular relationship
- Wrong theorem application
- Length comparison mistakes
- Observation errors in diagrams
- Assumption-based solving without verification
Students should solve geometry questions carefully and logically instead of depending completely on memorization.
Understanding Tangents and Circle Properties in Simple Language
A tangent is a straight line that touches a circle at exactly one point.
The point where the tangent touches the circle is called the point of contact.
One of the most important concepts in this chapter is that the radius drawn to the point of contact is always perpendicular to the tangent.
For example:
if a tangent touches a circle at point P,
then the radius joining the center and point P forms a 90° angle with the tangent.
Students also learn that if two tangents are drawn from the same external point outside the circle, then both tangent lengths are always equal.
This chapter becomes much easier when students focus on understanding geometric relationships visually instead of memorizing theorem statements only.
Important Theorems Used in Circles
The following theorems are extremely important for board exams and competency-based objective questions.
| Theorem | Explanation |
|---|---|
| Radius-Tangent Theorem | Radius drawn to the point of contact is perpendicular to the tangent |
| Equal Tangents Theorem | Tangents drawn from the same external point are equal in length |
Students should revise these theorems regularly because many MCQs are directly concept based.
Important Terms Used in Circles
The following geometry terms are very important in this chapter.
| Term | Meaning |
|---|---|
| Tangent | A line touching the circle at one point |
| Point of Contact | Point where tangent touches the circle |
| Radius | Line joining center and circle boundary |
| External Point | Point outside the circle from where tangents are drawn |
| Perpendicular | Angle of 90° formed between radius and tangent |
Understanding these terms properly helps students solve theorem-based questions much faster.
Geometry Observation Skills in Circles
One of the most important skills in this chapter is observing geometric relationships carefully inside the figure.
Students can improve circle understanding by:
- Observing tangent positions carefully
- Identifying right angles properly
- Understanding external point relationships
- Practicing theorem-based diagrams regularly
- Comparing tangent lengths logically
Once students become comfortable with diagram interpretation and geometric reasoning, theorem-based questions become much easier to solve.
Quick Memory Notes for Circles
Students should revise these important points regularly before exams:
- Tangent touches circle at one point only
- Point where tangent touches is called point of contact
- Radius is perpendicular to tangent
- Tangents from same external point are equal
- Diagram observation is very important
- Geometry reasoning improves accuracy
- Theorem understanding is more important than memorization
Short revision sessions improve geometry confidence and board exam preparation significantly.
Final Summary
Practicing Circles MCQs Class 10 with Answers is one of the best ways to improve theorem understanding, geometry reasoning, and diagram interpretation skills for Class 10 Maths. This chapter is highly conceptual because students must understand circle properties, tangent relationships, and geometric logic together instead of focusing only on formulas. Students preparing for CBSE board exams should focus on theorem clarity, careful observation, and regular objective practice to improve confidence and problem-solving speed naturally. Consistent practice helps students strengthen logical reasoning, conceptual understanding, geometry visualization, and overall board exam performance effectively.