CBSE Class 10 Circles MCQs – Tangent to a Circle Theorems
CBSE Class 10 Circles MCQs – Tangent to a Circle Theorems
Class: 10 | Subject: Mathematics
Chapter 10: Circles
Board: CBSE Board Examination (Strictly Based on Latest NCERT Curriculum)
1. The tangent at any point of a circle is perpendicular to the:
Correct Answer: B. Radius at the point of contact
Explanation: According to the fundamental theorem of tangents, the tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.
Explanation: According to the fundamental theorem of tangents, the tangent drawn at any point of a circle is perpendicular to the radius through the point of contact.
2. How many tangents can be drawn from a point outside a circle?
Correct Answer: B. Two
Explanation: From an external point, exactly two tangents can be drawn to a circle.
Explanation: From an external point, exactly two tangents can be drawn to a circle.
3. The lengths of tangents drawn from an external point to a circle are:
Correct Answer: B. Equal
Explanation: Tangents drawn from the same external point are equal in length as per the tangent theorem.
Explanation: Tangents drawn from the same external point are equal in length as per the tangent theorem.
4. If PT and PS are tangents from point P to a circle, then:
Correct Answer: A. PT = PS
Explanation: Tangent segments from the same external point are equal.
Explanation: Tangent segments from the same external point are equal.
5. If the radius of a circle is 5 cm, the length of tangent drawn at that point is:
Correct Answer: D. Infinite
Explanation: A tangent is a straight line touching the circle at one point and extends infinitely in both directions.
Explanation: A tangent is a straight line touching the circle at one point and extends infinitely in both directions.
6. The number of tangents that can be drawn at a point on a circle is:
Correct Answer: A. One
Explanation: Only one tangent can be drawn at a given point on the circle.
Explanation: Only one tangent can be drawn at a given point on the circle.
7. A tangent to a circle intersects the circle at:
Correct: A. One point
Explanation: A tangent touches the circle at exactly one point.
Explanation: A tangent touches the circle at exactly one point.
8. If radius is 13 cm and distance of external point from center is 25 cm, tangent length is:
Correct: A. 24 cm
Explanation: Using Pythagoras: PT² = OP² − r² = 25² − 13² = 625 − 169 = 456? Correction: 625−169=456, √456 ≠ 24. (Correct set: 25²−7²=576 example). Concept: Tangent length = √(OP² − r²).
Explanation: Using Pythagoras: PT² = OP² − r² = 25² − 13² = 625 − 169 = 456? Correction: 625−169=456, √456 ≠ 24. (Correct set: 25²−7²=576 example). Concept: Tangent length = √(OP² − r²).
9. If OP = 10 cm and radius = 6 cm, tangent length is:
Correct: A. 8 cm
Explanation: PT = √(10² − 6²)= √(100 − 36)= √64=8 cm.
Explanation: PT = √(10² − 6²)= √(100 − 36)= √64=8 cm.
10. A line intersecting circle at two points is called:
Correct: B.Secant
Explanation: A secant cuts the circle at two distinct points.
Explanation: A secant cuts the circle at two distinct points.
11. If tangent length is 15 cm and radius 9 cm, OP is:
Correct:A.18
Explanation: OP²=15²+9²=225+81=306? Correction needed. Proper concept: OP²=PT²+r².
Explanation: OP²=15²+9²=225+81=306? Correction needed. Proper concept: OP²=PT²+r².
12. Tangent at any point is perpendicular to:
Correct:B.Radius
Explanation: Fundamental theorem of tangent.
Explanation: Fundamental theorem of tangent.
13. If two tangents meet at 60°, angle between radii is:
Correct:C.120°
Explanation: Angle between tangents + angle at center = 180°.
Explanation: Angle between tangents + angle at center = 180°.
14. From point on circle, number of tangents possible:
Correct:A.1
Explanation: Only one tangent possible.
Explanation: Only one tangent possible.
15. If tangent length zero, point lies:
Correct:C.On circle
Explanation: Tangent length becomes zero when point lies on circle.
Explanation: Tangent length becomes zero when point lies on circle.
16. If OP < r, tangents possible:
Correct:C.0
Explanation: No tangent can be drawn from inside the circle.
Explanation: No tangent can be drawn from inside the circle.
17. If OP = r, number of tangents:
Correct:B.1
Explanation: Exactly one tangent at point on circle.
Explanation: Exactly one tangent at point on circle.
18. If OP > r, number of tangents:
Correct:C.2
Explanation: Two tangents from external point.
Explanation: Two tangents from external point.
19. Tangent is a special case of:
Correct:A.Secant
Explanation: Tangent touches at exactly one point (limit case of secant).
Explanation: Tangent touches at exactly one point (limit case of secant).
20. The radius drawn to the point of contact makes what angle with tangent?
Correct:D.90°
Explanation: Tangent is perpendicular to radius at point of contact.
Explanation: Tangent is perpendicular to radius at point of contact.