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