Question

In the adjoining figure, AB and AC are two equal chords of a circle of radius 5 cm . If AB = AC = 6 cm , find the length of chord BC

Answer 1

Let $OD=xcm$

Then $AD=(5-x)cm$

Now in triangle $BOD$,

$BO=4cm,OD=xcm$

Then by pythagoras theorem,

$B{D}^2=B{O}^2-O{D}^2$

$B{D}^2=16-x^2$ ......................1

Now in triangle$BAD$

$BA=6cm,AD=(5-x)cm$

Then by pythagoras theorem,

$B{D}^2=B{A}^2-A{D}^2$

$B{D}^2=36-(5-x{)}^2$ ....................2

As equation 1=2

Thertefore,$16-x^2=36-25-x^2+10x$

$x=\frac{1}{2}cm$

Hence,$B{D}^2=16-(\frac{1}{2}{)}^2$

$BD=\frac{\sqrt{63}}{2}cm$

Therefore $BC=\sqrt{63}$cm