JAMB Mathematics 1982 Question 50

Question 50

Circle Theorems

TP and TQ are tangents to a circle O and R is a point on the circumference of the circle as shown, in the figure. If angle PTQ = 45°, what is the magnitude of the angle PRQ?

A.45°
B.135°
C.40°
D.67½°
E.52½°.

Show the answer and explanation

Answer: D (67½°)

Explanation

Tangents from T are equal, so <TPQ = <TQP = (180° − 45°)/2 = 67½°. By the alternate segment theorem <PRQ = <TQP = 67½°.