Problem Solving (PS) | Re: P, Q, S, and R are points on the circumference of a circle of radius r

Please refer to attached figure.

Diameter PS divides the Quadrilateral PQSR into two SIMILAR RIGHT TRIANGLES

Since, the triangle PQR is an equilateral triangle, therefore angle subtended by each arc: QP = PR = SQ = 120

△QOP is an Isosceles Triangle with sides OP = OQ = r and ∠QOP = 120, therefore, ∠QPO = ∠OQP = 30

△PQS is a Right Triangle with ∠PQS = 90 because the chord PS (Diameter) subtends 180 degree at the center therefore angle subtended in the remaining arc will be half of
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