wiz-icon
MyQuestionIcon
MyQuestionIcon
1
You visited us 1 times! Enjoying our articles? Unlock Full Access!
Question

In the figure, PQR=100, where P, Q and R are points on a circle with centre O. Find OPR.

A
20
No worries! We‘ve got your back. Try BYJU‘S free classes today!
B
10
Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses
C
30
No worries! We‘ve got your back. Try BYJU‘S free classes today!
D
15
No worries! We‘ve got your back. Try BYJU‘S free classes today!
Open in App
Solution

The correct option is B 10

Consider the cyclic quadrilateral PQRM.
Since opposite angles are supplementary in a cyclic quadrilateral, we have
PQR+PMR=180
PMR=180PQR=180100=80.

Since the angle subtended by an arc of a circle at its centre is twice the angle subtended by the same arc at a point on the remaining part of the circle and since PMR=80, we have
POR=2×PMR=2×80=160.

Now, consider the OPR, which is isosceles as OP=OR=radii of the circle.
OPR=ORP
But by angle sum property, we have
OPR+ORP+POR=180.
2OPR+POR=180
2OPR=180POR=180160=20
OPR=10


flag
Suggest Corrections
thumbs-up
2
Join BYJU'S Learning Program
similar_icon
Related Videos
thumbnail
lock
Cyclic Quadrilateral
MATHEMATICS
Watch in App
Join BYJU'S Learning Program
CrossIcon