Question

O is the centre of the circle as shown in the figure, $\angle ORP={35}^{\circ }$ and the distance between P and Q through 'O' is 4 cm. What is the measure of $\angle ROQ$?

• A. ${70}^{\circ }$
• B. ${105}^{\circ }$
• C. ${55}^{\circ }$
• D. ${35}^{\circ }$

Answer 1

The correct option is A

${70}^{\circ }$

Since line segment PQ passes through the centre O, so PQ is the diameter of the circle.

$PQ=4cm=2\times OQ=2\times$ radius,
On joining $RQ.\angle PRQ={90}^{\circ }$ [$\because$ Angle subtended by diameter on the circle is ${90}^{\circ }$]
$\therefore \angle ORQ={90}^{\circ }-{35}^{\circ }={55}^{\circ }$
But, $OR=OQ$
$\therefore \angle ORQ=\angle OQR={55}^{\circ }$
$\therefore y={180}^{\circ }-({55}^{\circ }+{55}^{\circ })={70}^{\circ }$ [Sum of angles of a triangle is ${180}^{\circ }$]