Q. 2

# 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.

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.

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