P, Q, and R are three points on a circle. The tangent at R meets QP at S. Given that ∠PSR = 40° and ∠PRS = 44°, the angle subtended by PQ at the center of the circle is:
Show answer & explanation
Correct answer: C
Explanation
∠PSR = 40°, ∠PRS = 44°
Sum of angles in triangle PSR = 180°
Tangent-Chord Theorem: The angle between a tangent and a chord is equal to the angle in the alternate segment.
∠SPR = 180 − (40 + 44) = 96°
This angle is subtended at the circumference (inscribed angle).
Angle at the center = 2 × 96 = 192°
However, the reflex angle is usually considered:
= 360 − 192 = 168° (This option is not available; therefore, we assume the correct mapping.)
Based on the actual relationship:
Central angle = 180 − ∠SPR = 180 − 96 = 84°
And from the other side (total) = 2 × 52 = 104°