#### Question

In the figure given below, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60°, find ∠PRQ.

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#### Solution

m∠OPT 90^{º} (radius is perpendicular to the tangent)

So, ∠OPQ = ∠OPT - ∠QPT

= 90º - 60º

= 30º

m∠POQ = 2m∠QPT = 2 x 60º = 120º

reflex m∠POQ = 360º - 120º= 240º

`/_PQR=1/2 "reflex"/_POQ`

`=1/2 xx 240^@`

`=120^@`

`m/_PRQ=120^@`

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#### Reference Material

Solution for question: In the figure given below, PQ is a chord of a circle with centre O and PT is a tangent. If ∠QPT = 60°, find ∠PRQ. concept: null - Tangent to a Circle. For the course CBSE