Question

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

Answer 1

Given Two circles have the same center O and AB is a chord of the larger circle touching the smaller circle at C; also. OA = 5 cm and OC = 3 cm

in △OAC,OA² = OC² + AC²

∴ AC² = OA² - AC²

\(\Rightarrow\) AC² = 5² - 3²

\(\Rightarrow\) AC² = 25 - 9

\(\Rightarrow\) AC² = 16

\(\Rightarrow\) AC = 4cm

∴ AB = 2AC (Since perpendicular drawn from the center of the circle bisects the chord)

∴ AB = 2 x 4 = 8 cm

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