Question

O is the centre of a circle. If PS = QR, ∠PQS = 24°, find ∠QPR, ∠OSQ and ∠POS.

Answer 1

Step 1:

Since PS = QR, the angles subtended by these chords at the circumference are equal.

∠QPR = ∠PQS

∠QPR = 24°

Step 2:

The angle subtended by arc PS at the center is ∠POS

The angle subtended by arc PS at the circumference is ∠PQS

∠POS = 2 × ∠PQS

∠POS = 2 × 24° = 48°

Step 3:

Consider ΔOSQ

OS = OQ (radii of the same circle).

Therefore, ΔOSQ is an isosceles triangle.

∠OSQ = ∠OQS

We know ∠OQS = ∠PQS = 24°

So, ∠OSQ = 24°

The measures of the angles are ∠QPR = 24°, ∠OSQ = 24° and ∠POS = 48°.