The radius of a circle is 40 cm and the length of perpendicular drawn from its centre to chord is 24 cm. Find the length of chord.

From figure,

Given: Radius of the circle (r) = 40 cm

AC is the chord and OB is the perpendicular distance from center.

B is the midpoint of AC, as OB is perpendicular to the chord AC.

AB = $\dfrac{1}{2}$ AC

In Δ OAB, ∠B = 90°

Using Pythagoras theorem,

∴ OA² = OB² + AB²

⇒ (40)² = (24)² + AB²

⇒ 1600 = 576 + AB²

⇒ AB² = 1600 - 576

⇒ AB² = 1024

⇒ AB = $\sqrt{1024}$

⇒ AB = 32 cm

Length of the chord = AC = 2(AB)

= 2(32)

= 64 cm.

Hence, the length of the chord is 64 cm.