In fig. $O$ is centre of circle and $O C$ is bisector of $∠ A C B$ . If $A C = 4 c m$ , tien find $B C$ .

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Solution

Join $O A$ and $O B$
In $Δ O C A$ and $Δ O C B$
$O A = O B$ (Same radius of circle)
$O C = O C$ (common)
$∠ A C O = ∠ B C O$
( $∵ O C$ , is bisector of $∠ A C B$ )
Thus, by SAS congruence criterion
$Δ O C A = Δ O C B$
By CPCT
$A C = B C = 4$
$4 = B C$
or $B C = 4 c m$

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