Question

If r1, and r2, are the radii of two concentric circles and (r1>r2) If the chord
of the larger circle AB touches the inter circle. Find the value of AB​

Answer 1

Given : r1 and r2 are the radii of two concentric circles and r1> r2

AB is chord of larger circle touches the inner circle

To Find : Length of AB

Solution:

AB is chord of circle

and touches other circle , let say at M

and O is center of both circles

Then   OM⊥ AB   ( as AB is tangent)

also AB is chord  hence M is mid point of AB

AM² = OA² - OM²

OA = r₁   ( radius of larger circle)

OM = r₂ ( radius of smaller circle)

=> AM² = r₁² - r₂²

AM =  √(r₁² - r₂²)

AB = 2AM  = 2 √(r₁² - r₂²)

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