Question

In Fig. 9, O is the centre of the circle. The distance between P and Q is 4 cm. Find the ∠ROQ.

Answer 1

Given: A circle with centre O and radius OQ = 2 cm; and PQ = 4 cm.

Construction: Join OP.

As, OQ = 2 cm and PQ = 4 cm

So, PQ is the diameter of the circle.

In $∆$OPR,

Since, OP = OR (Radii)

So, ∠OPR = ∠ORP (Angles opposite to equal sides are equal)

$\Rightarrow$∠OPR = 35$°$

$\Rightarrow$∠QPR = 35$°$

Now,

As, the subtended by an arc at the centre is double the angle subtended by the same arc at the remaining part of the circle.

So, ∠ROQ = 2∠QPR = 2 $\times$ 35$°$ = 70$°$