The Circles chapter in Class 10 Maths helps students understand important geometric concepts such as tangents, points of contact, and the relationship between radii and tangents. These concepts develop logical reasoning, diagram interpretation, and theorem application skills. Regular practice of Circles MCQs Class 10 helps students improve accuracy and prepare for competency-based objective questions in CBSE board exams.
A clear understanding of circle theorems makes it easier to solve geometry problems and apply concepts confidently. Students can practice chapter-wise MCQs and revise through Class 10 MCQs to strengthen their preparation. They can also explore CBSE Board resources and MCQs Class 10 Maths for objective practice based on the latest syllabus and exam pattern.
Topics Covered
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
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Class 10 Chapter 10 Circles MCQs with Answers
Check your understanding of Circles by solving these MCQs for Class 10 Maths. These objective questions help students improve theorem understanding, geometric reasoning, tangent concepts, and board exam preparation skills effectively.
Q1. 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.
Q2. 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.
Q3. 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.
Q4. 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.
Q5. 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.
Q6. 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.
Q7. 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.
Q8. 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.
Q9. 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.
Q10. 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.
Q11. 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.
Q12. 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.
Q13. 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.
Q14. 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.
Q15. 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.
Q16. 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.
Q17. 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.
Q18. 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.
Q19. 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.
Q20. 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.
Q21. 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.
Q22. 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.
Q23. 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.
Q24. 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.
Q25. 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.
Q26. 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.
Q27. 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.
Q28. 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.
Q29. 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.
Q30. 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
