A chord of a circle of radius 10 cm subtends a right angle at its centre. The length of the chord (in cm) is

Question

Philoid · Accepted Answer

Let PQ be the chord of a circle subtending a right angle at the centre of the circle.

Also, radius of circle = OP = OQ = 5 cm

Now, Δ OPQ is a right angled triangle.

We know that by Pythagoras Theorem, AC² = AB² + BC²

In Δ OPQ, PQ² = OP² + OQ²

⇒ PQ² = 5² + 5²

⇒ PQ² = 25 + 25

⇒ PQ² = 50

⇒ PQ = 5√2

∴ The length of the chord is 5√2 cm.