Question

Two concentric circles are of radii 12 cm and 13 cm. Find the length of the chord of the outer circle which touches the inner circle.

Answer 1

The two circles have the same centre O.

Radius of inner circle = 12 cm

Radius of outer circle = 13 cm

A chord of the outer circle touches the inner circle.

So the chord is tangent to the inner circle.

Therefore, the perpendicular distance from the centre to this chord equals the inner radius:

Distance from centre to chord = 12 cm

Let the chord belong to the outer circle (radius 13 cm).

Let half the chord length be x.

x² + 12² = 13²

x² = 169 − 144 = 25

x = 5 cm

Chord length = 2x = 2 × 5

= 10 cm