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Two circles whose radii are equal to 4 a...

Two circles whose radii are equal to 4 and 8 intersect at right angles. The length of their common chord is-

A

`(16)/(sqrt(15))`

B

8

C

`4sqrt(6)`

D

`(8sqrt(5))/(5)`

Text Solution

Verified by Experts

The correct Answer is:
A

`C_(1)C_(2)=sqrt(16+64)=4sqrt(5)`
`PM = PC_(1)sin theta`
`= PC_(1)xx(PC_(2))/(C_(1)C_(2))=4xx(8)/(4sqrt(5))=(8)/(sqrt(5))`
`PQ=2(PM)=(16)/(sqrt(5))`
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