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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. - Mathematics

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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 90º (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^@`

Concept: Tangent to a Circle
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