Question

Tangents PQ and PR are drawn to the circle from an external point P. If PQ = 9 cm, and . Find the length of the chord QR.

Answer 1

We know that the lengths of tangents drawn from an external point to a circle are equal.

∴PQ = PR

In ΔPQR, PQ = PR

⇒ ∠PRQ = ∠PQR = 60° (Equal sides have equal angles opposite to them)

Now, ∠PRQ + ∠PQR + ∠QPR = 180° (Angle sum property)

60° + 60° + ∠QPR = 180°

120° + ∠QPR = 180°

∠QPR = 180° − 120° = 60°

∴∠PRQ = ∠PQR = ∠QPR = 60°

Thus, ΔPQR is an equilateral triangle.

Hence, the length of chord QR is 9 cm.