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Question

# AB and AC are two chords of a circle such that AB=AC=6 cm. If radius of the circle is 5 cm, then BC is:

A
4.8 cm
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B
9.6 cm
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C
2.4 cm
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D
8.4 cm
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Solution

## The correct option is B 9.6 cmAccording to the question:fromtheusingpythogorustheorum:⇒(BC2)2=AB2−(r−x)2=36−(r−x)2−−−−(i)⇒(BC2)2=r2−x2−−−−−−(ii)⇒36−(r−x)2=r2−x2⇒36−(r2+x2−2rx)=r2−x2⇒36−r2−x2+2rx=r2−x2⇒2rx=2r2−36⇒x=r2−18r=25−185=75Now,substitutexinequ(ii)⇒(BC2)2=r2−x2=52−(75)2=25−4925=625−4925=57625⇒(BC2)=√57625=245⇒BC2=245⇒BC=485=9.6cmsothatcorrectoptionisB.

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