Question

if the bisectors of the opposite angles angle p and angle r of a cyclic quadrilateral PQRS intersect the corresponding circle at A and B respectively then AB is a diameter of the circle. prove that.

Answer 1

Answer:

Step-by-step explanation:

Plz refer to attached diagram.

PQRS is cyclic quadrilateral.

∠ P + ∠R = 180° -- Opposite angles are supplementary

AP and CQ are bisector for ∠A and ∠C respectively.

∴ 1/2 ∠ APS + 1/2 ∠SRB = 90°

∠SRB = ∠SPB -- Angles in same segment are equal

∴ ∠APS + ∠SPB = 90°

∴ ∠APB = 90°

∠APB is in semicircle.

Hence, AB is a diameter of the circle.

Answer 2

Step-by-step explanation:

hope this will help you