wiz-icon
MyQuestionIcon
MyQuestionIcon
2
You visited us 2 times! Enjoying our articles? Unlock Full Access!
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 the value of PTR.

Open in App
Solution

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

flag
Suggest Corrections
thumbs-up
0
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Terms Related to Circles
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon