2020 · Q63
ABCD is a cyclic quadrilateral. The bisectors of the angles A, B, C and D cut the circle at P, Q, R and S respectively. What is ∠PQR + ∠RSP equal to?
Elementary MathematicsCircles
- A90°
- B135°
- C180°
- D270°
Explanation
P, Q, R, S lie on the circumcircle of ABCD, so PQRS is a cyclic quadrilateral and opposite angles sum to 180 degrees. Hence option (C). Any pair of opposite angles of a cyclic quadrilateral sums to 180 degrees.