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Question

Two tangents TP and TQ are drawn to a circle with centre O from an external point T. Find PTQ2OPQ.

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Solution

The length of tangents drawn from an internal point to a circle are equal.
Thus, TP=TQ
TQP=TPQ(Angle opposite to equal sides are equal)
As we know,
PT is tangent, & OP is radius.
OPTP(Tangent at any point of circle is perpendicular to the radius through point of contact.)
So, OPT=90°

OPQ+TPQ=90

TPQ=90OPQ

InPTQ

TPQ+TQP+PTQ=180°

TPQ+TPQ+PTQ=180°
TPQ+PTQ=180°(from (1)YQP=TPQ)
2(90°OPQ)+PTQ=180°

180°2OPQ+PTQ=180°

PTQ=180180+2OPQ

PTQ=2OPQ

955818_317900_ans_0ca7904e33684449aa7b0bf8a4b334e8.jpg

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