Two concentric circles having radii 73 and 55 are given. The chord of the circle with larger radius touches the circle with smaller radius. Find the length of the chord.

Question

Philoid · Accepted Answer

Given the radius of larger circle = 73 = OB and radius of smaller circle = 55 = OM

Since AB is a tangent, OM ⊥ AB.

Consider ΔOMB,

Here, ∠OMB is a right angle.

By Pythagoras Theorem,

⇒ OB² = OM² + MB²

⇒ MB² = OB² – OM²

= 73² – 55²

We know that a² – b² = (a + b) (a – b)

⇒ MB² = (73 + 55) (73 – 55)

= (128) (18)

= 2304

∴ MB = 48

Now, length of chord = AB = 2MB = 2 (48) = 96

∴ The length of chord is 96.