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Circles
CBSE 2026 Board Exam Set 1 (Code 30/7/1)
CBSE_BOARD_PYQ_2026_30_7_1
Grade 10
Question:
[Section A]
In the given figure, $PA$ and $PB$ are tangents to the circle with center $O$. If $OP = 10$ cm and $\angle APB = 60^\circ$, then length of $PA$ is:
(A) $5$ cm
(B) $5\sqrt{3}$ cm
(C) $5/\sqrt{3}$ cm
(D) $10$ cm
In the given figure, $PA$ and $PB$ are tangents to the circle with center $O$. If $OP = 10$ cm and $\angle APB = 60^\circ$, then length of $PA$ is:
(A) $5$ cm
(B) $5\sqrt{3}$ cm
(C) $5/\sqrt{3}$ cm
(D) $10$ cm
Step-by-Step Solution
Key Concept: In right $\triangle PAO$, $\angle APO = 30^\circ$. $\cos 30^\circ = PA / OP \Rightarrow PA = OP \cos 30^\circ$.
Sol. (A) $5$ cm. [1.0 Mark]
Correct Answer: (A) $5$ cm
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