Vardaan Learning Institute

Answer Key: Circles PYQ

Class: 10 (CBSE) Subject: Mathematics Chapter: 10

BOARD EXAM 2025 (Set 30/6/3)

Q1. For a circle with centre O and radius 5 cm, which of the following statements is true?

(A) Distance between every pair of parallel tangents is 5 cm.
(B) Distance between every pair of parallel tangents is 10 cm.
(C) Distance between every pair of parallel tangents must be between 5 cm and 10 cm.
(D) There does not exist a point outside the circle from where length of tangent is 5 cm.

Q2. In figure, AP and AQ are tangents with centre O. If reflex \(\angle POQ = 210�\), the value of \(2x\) is

Q18. In figure, PA and PB are tangents with \(\angle P = 90�\). If \(AB = 3\sqrt{2}\) cm, then the diameter is

Q29. In figure, TP and TQ are tangents. If \(\angle OPQ = 15�\) and \(\angle PTQ = \theta\), find \(\sin 2\theta\).

\(\angle POQ = 180 - 30 = 150�\). \(\theta = 180 - 150 = 30�\). \(\sin 2\theta = \sin 60� = \frac{\sqrt{3}}{2}\).