Question 49

Let PQRS be a cyclic quadrilateral. Let O be the centre of the circumcircle of the quadrilateral. Then which of the following statements is NOT true?

Solution

The angle which an arc of a circle subtends at the centre is double that which it subtends at any point on the remaining part of the circumference.

$$\angle\ POQ=2\angle\ PSQ$$

Angles in the same segment of a circle are equal to one another

$$\angle\ PRQ=\angle\ PSQ$$

OPS is isosceles ( OP =OS =radius)

$$\angle\ OPS=\angle\ OSP$$

$$\angle\ PRQ\ \ne\ \angle\ POQ$$

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