In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that ∠ QAP + ∠ APR = 90° .

CBSE Class 10 Maths PYQ · Circles · Find angles · 3 Marks · March 2023 · Standard

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623 Marks · March 2023 · Standard

In the given figure, O is the centre of the circle and QPR is a tangent to it at P. Prove that $\angle QAP + \angle APR = 90^\circ$.

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OA = OP
$\therefore$ In $\triangle OAP$, $\angle OPA = \angle OAP$ ... (i)
$\angle OPA + \angle APR = 90^\circ$
$\Rightarrow \angle OAP + \angle APR = 90^\circ$ Using (i)
$\Rightarrow \angle QAP + \angle APR = 90^\circ$