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Question

In the given figure, PT is a tangent drawn from an external point T to the circle with centre O and PQ is the diameter of the circle. Point Q and T are joined by a line which is intersecting the circle at R. IfPOR=78, then find PTR.

A
39
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B
51
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C
61
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D
41
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Solution

The correct option is B 51
In, OQR,
OQ=OR (Radius)
(Angles opposite to equal sides are equal.)
OQR=ORQ

By exterior angle property,
POR=OQR+ORQ78=2OQROQR=39PQR=OQR=39

We know that, tangent at any point is perpendicular to the radius at the point of contact.
TPQ=90

Now, consider TPQ,
TPQ+PQR+QTP=180
QTP=1803990
QTP=PTR=51

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