Try each question on your own first. Use the Show Answer button only after you have selected your option, then read the explanation and revise the related concept from your chapter notes.
19. If angle between two tangents drawn from P to circle with radius r and centre O is 60°, then length of OP is:
A. r
B. 2r
C. r√3
D. r/2
Answer: B. 2r
Explanation: sin 30° = r / OP ⇒ 1/2 = r / OP ⇒ OP = 2r.
20. The angle between two tangents drawn from an external point to a circle is _____ to angle subtended by line-segment joining points of contact at centre.
A. Equal
B. Complementary
C. Supplementary
D. Half
Answer: C. Supplementary
Explanation: The sum of these two angles is 180°, which makes them supplementary.
21. Line segment joining centre to point of contact of tangent is always _____ to tangent.
A. Parallel
B. Perpendicular
C. Equal
D. Coincident
Answer: B. Perpendicular
Explanation: Standard Theorem 10.1: Radius is perpendicular to tangent at point of contact.
22. If length of tangent from point A at distance 5 cm from centre is 4 cm, radius of circle is:
A. 3 cm
B. 4 cm
C. 5 cm
D. 9 cm
Answer: A. 3 cm
Explanation: r = √(5² - 4²) = √(25 - 16) = √9 = 3 cm.
23. Total number of tangents that can be drawn to a circle from a point on its circumference is:
A. 0
B. 1
C. 2
D. Infinite
Answer: B. 1
Explanation: Exactly one tangent passes through a specific point lying on the circle.
24. In a right triangle ABC right angled at B, BC = 6 cm and AB = 8 cm. A circle is inscribed in ΔABC. Radius of circle is:
A. 1 cm
B. 2 cm
C. 3 cm
D. 4 cm
Answer: B. 2 cm
Explanation: Hypotenuse AC = √(6² + 8²) = 10 cm. Inradius r = (a + b - c)/2 = (6 + 8 - 10)/2 = 4/2 = 2 cm.
25. If PT is tangent to circle with centre O and radius 6 cm such that PT = 8 cm, then OP is:
A. 10 cm
B. 12 cm
C. 14 cm
D. 7 cm
Answer: A. 10 cm
Explanation: OP = √(6² + 8²) = √(36 + 64) = √100 = 10 cm.
26. Concentric circles are circles having the same:
A. Radius
B. Diameter
C. Centre
D. Circumference
Answer: C. Centre
Explanation: Circles having same centre but different radii are called concentric circles.
27. If PA and PB are tangents from P to a circle with centre O and ∠AOB = 130°, then ∠APB is:
A. 40°
B. 50°
C. 60°
D. 70°
Answer: B. 50°
Explanation: ∠APB = 180° - 130° = 50°.
28. A line touching a circle at one point only is called a:
A. Secant
B. Tangent
C. Chord
D. Segment
Answer: B. Tangent
Explanation: Definition of tangent: A straight line touching a circle at exactly one point.
29. Tangents drawn at the ends of a diameter of a circle are:
A. Perpendicular
B. Parallel
C. Intersecting
D. Equal in length
Answer: B. Parallel
Explanation: Both tangents are perpendicular to the diameter, so alternate interior angles are 90°, making them parallel.
30. If length of a tangent from a point P to a circle of radius 9 cm is 12 cm, distance of P from centre is:
This page contains a chapter-wise objective practice set. Try the questions without checking the answer first, then use the explanation to understand the point you missed. The current page contains 30 questions, so you can practise in smaller sets when you are revising.
Quick revision tip
After the practice set, write down the question numbers you missed and revise only those concepts once more. This makes MCQ practice more useful than repeatedly attempting the same questions without reviewing mistakes.
