In a circle with centre O, PQ and QR are two chords such that ∠PQR = 118°. What is the measure of ∠OPR?
Show answer & explanation
Correct answer: A
Explanation
The correct answer is option 1 i.e. 28°
Let P and R meet at point S on the major segment of the circle
Now, PQRS is a cyclic quadrilateral
So, ∠PSR + ∠PQR = 180°
⇒ ∠PSR + 118 = 180°
⇒ ∠PSR = 62°
Now, ∠POR = 124°
OP = OR = radius of the circle
So, ∠OPR = (180 - 124)/2
⇒ ∠OPR = 28°