Ex 9.3, 3
In the given figure, PQR = 100 , where P, Q and R are points on a circle with centre O. Find OPR.
Here, PR is chord
We mark point S on the major arc of the circle.
PQRS is a cyclic quadrilateral.
So, PQR + PSR = 180
100 + PSR = 180
PSR = 180 100
PSR = 80
Arc PQR subtends POR at centre of circle.
And PSR on point S
So, POR = 2 PSR
POR = 2 (80 ) = 160
Now,
In OPR
OP = OR
OPR = ORP
Also, in OPR
OPR + ORP + POR = 180
OPR + OPR + POR = 180
2 OPR + 160 = 180
2 OPR = 180 160
2 OPR = 20
OPR = (20 )/2
OPR = 10

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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