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Circles
CBSE 2026 Board Exam Set 3 (Code 30/1/3)
CBSE_BOARD_PYQ_2026_30_1_3
Grade 10
Question:
[Section A]
In the given figure, $PA$ and $PB$ are tangents to a circle with centre $O$ from an external point $P$. If $\angle APB = 110^\circ$, then $\angle AOB$ is:
(a) $55^\circ$
(b) $70^\circ$
(c) $110^\circ$
(d) $35^\circ$
In the given figure, $PA$ and $PB$ are tangents to a circle with centre $O$ from an external point $P$. If $\angle APB = 110^\circ$, then $\angle AOB$ is:
(a) $55^\circ$
(b) $70^\circ$
(c) $110^\circ$
(d) $35^\circ$
Step-by-Step Solution
Key Concept: $\angle AOB + \angle APB = 180^\circ \Rightarrow \angle AOB = 70^\circ$.
$\angle AOB = 180^\circ - 110^\circ = 70^\circ$. $\angle AOP = 35^\circ$. [1.0 Mark]
Correct Answer: (b) 70° (or (d) 35° if asking for half angle ∠AOP)
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