Question

In the adjoining figure, A and B are the centres of two circles. If CB=17cm, EB=15cm, then find the length of common chord.

Answer 1

The linc segment joining the centres of the circles bisect the common chord at right angle
`thereforeangle BEC=90^@`
In `DeltaBEC`,
`BE^2+EC^2=BC^2` (by Pythagoras theoram)
`rArrEC^2=BC^2-BE^2=17^2-15^2=289-225=64`
`rArrEC=sqrt(64)=8cm`
Now, `CD=2EC` (Property 1)
`=2xx8=16 cm`
`therefore` Length of common chord= 16 cm .