Question

for two concentric circle of radius 25 cm and 17 cm ; the chord of the larger circle touches the smaller circle . find its length ​

Answer 1

Given : two concentric circle of radius 25 cm and 17 cm  

chord of larger circle touches the smaller circle

To Find : Length of Chord

Solution:

Let say 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 = 25  ( radius of larger circle)

OM = 17 ( radius of smaller circle)

=> AM² = 25² -17²

=> AM² = 336

=> AM = 4√21

=> AM = 18.33  

AB = 2AM  = 2*18.33   = 36.66 cm  

Length of Chord = 36.66 cm     or 8√21 cm

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