Question

Two concentric circles are of radii 5 cm and 3 cm. Find the length of the chord of the larger circle which touches the smaller circle.

Answer 1

Let the two concentric circles with centre O.

AB be the chord of the larger circle which touches the smaller circle at point P. 

∴ AB is tangent to the smaller circle to the point P.

⇒ OP ⊥ AB
By Pythagoras theorem in ΔOPA,
OA² =  AP² + OP²
⇒ 5² = AP² + 3²
⇒ AP² = 25 - 9
⇒ AP = 4
In ΔOPB,
Since OP ⊥ AB,
AP = PB (Perpendicular from the center of the circle bisects the chord)
AB = 2AP = 2 × 4 = 8 cm

∴ The length of the chord of the larger circle is 8 cm.