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Tangent at P with angle QPT given: find angle POQ

The same question, asked 2 times: CDS 1 2018*, CDS 1 2026. Every wording below, oldest first.

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  1. Question 1

    CDS 1 2018

    99
    In the figure given below, SPT is a tangent to the circle at P and O is the centre of the circle. If ∠QPT=α\angle QPT = \alpha, then what is ∠POQ\angle POQ equal to ?

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  2. Question 2

    CDS 1 2026

    63
    A triangle PQR is inscribed in a circle with its centre at O. A tangent PT is drawn at P such that ∠QPT=36∘\angle QPT = 36^\circ. What is ∠POQ\angle POQ equal to ?

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