Question

PQ is the chord of a circle whose centre is O. ROS is a line segment originating from a point R on the circle that intersect PQ produced at point S such that QS = OR. If ∠QSR = 30°, then what is the value (in degrees)of POR?

A) 30 B) 45 C) 60 D) 90

Answer 1

Answer:

90°                                                                                                                                                                                                                                            

Step-by-step explanation:

Give a circle with centre, O. A chord PQ to produced to S, such that ROS (R, being on the circumference) QS = OR. ∠QSR = 30 ° Find value of ∠POR.

QS = OR = OQ = being radii.

In isosceles triangle OQS, QS = OQ, so ∠QSO =∠QOS = 30°.

∠OQS = 180 - ∠QOS -∠QSO = 180–30–30 = 120 °

In isosceles triangle POQ,∠PQO = 60 deg, being supplementary of ∠OQS. ∠PQO =∠QPO = 60 °. So triangle POQ is equilateral.

∠POR = 180 - <QOS - ∠POQ = 180 - 30 - 60 = 90 °

Answer:∠POR = 90 °