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.
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)
∴ MB = 48
Now, length of chord = AB = 2MB = 2 (48) = 96
∴ The length of chord is 96.
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