Question

if radius of two concentric circles are 12cm and 13cm find the length of each chord of one circle which is tangent to the other circle​

Answer 1

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Answer 2

Given two concentric circles of radius $12$ and $13$ cm, Find the length of the chord of the outer circle which is tangent to the inner circle.

Explanation:

• Let the common center of the concentric circles be denoted by 'O'.
• Let the chord of the outer circle which is tangent to the inner circle be denoted by 'AB'.
• Let the point at which the chord is tangent to the inner circle be denoted by 'M'.
• We have the radii of the inner circle and the outer circle to be $12\ cm,\ 13\ cm$ respectively.
• Hence, we get $->OA=OB=13\ cm,\ \ \ ->OM=12\ cm$
• Since 'AB' is tangent to the inner circle we have, $\angle OMA=\angle OMB= \frac{\pi}{2}$  
• Hence in the triangles OMA and OMB we have,
•                  $->AM=MB=\sqrt{OB^2-OM^2}\\->AM=MB=\sqrt{13^2-12^2} \\->AM=MB=5\ cm$  
• Now the length of the chord AB is $AB=2AM=10\ cm$.
• The length of all the chords that are tangent to the inner circle is $10\ cm$.