Question

In the given figure, chords $AB=Ac=6cm$. if radius is $5cm$, the length of $BC$ is

Answer 1

REF.Image.

AB = AC = 6cm & radius = 5cm, BC = ?

$\because AB=AC$

$△OA$ is bisctor of $\angle BAC$

P divides BC in the ratio

$6:6\Rightarrow 1:1$

P is mid point of BC.

$OP\perp BC.$

Consider $△ABP$,

$(AB{)}^2=(AP{)}^2+(BP{)}^2$

$\Rightarrow (BP{)}^2=(6{)}^2-(AP{)}^2...(1)$

Also, $△OBP,$

$(OB{)}^2=(OP{)}^2+(BP{)}^2$

$(BP{)}^2=25-(5-AP{)}^2...\left(2\right)$

from equation (1)& (2),

$6^2-(AP{)}^2=25-(5-AP{)}^2$

$36-(AP{)}^2=25-25+(AP{)}^2+10AP$

$AP=3.6cm$

putting this value in (1), we get

$(BP{)}^2=36-(3.6{)}^2=23.04$

$BP=4.8cm$

$\therefore BC=BP+PC=2BP=2\times 4.8$

$=9.6cm$

$\Rightarrow BC=9.6cm$ Answer