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In a circle of radius 5 cm, AB and AC ar...

In a circle of radius `5 cm`, `AB` and `AC` are two chords such that `AB=AC=6 cm`. The length of chord `BC=`
(A) `4.8 cm`
(B) `9.6 cm`
(C) `2.4 cm`
(D) `5 cm`

Text Solution

Verified by Experts

`((BC)/2)^2=AB^2-(r-x)^2`
`=36-(r-x)^2----(1)`
`((BC)/2)^2=r^2-x^2-----(2)`
`36-(r-x)^2=r^2-x^2`
`36-(r^2-2rx+x^2)=r^2-x^2`
`36-r^2+2rx-x^2=r^2-x^2`
`2rx=2r^2-36`
`x=(2r^2-36)/2r`
...
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