Feb 10, 2018

Given that in $\Delta A B C , A B = A C$

$B X \mathmr{and} C Y$ are bisectors of $\angle A B C \mathmr{and} \angle A C B$ respectively.
So $\angle A B C = \angle A C B$
$B Y = 4 c m$, we are to find out length of $A X$

we have

$\angle A B C = \angle A C B$
$\implies \frac{1}{2} \angle A B C = \frac{1}{2} \angle A C B$

$\implies \angle A B X = \angle B C Y$

( since $B X \mathmr{and} C Y$ are bisectors of $\angle A B C \mathmr{and} \angle A C B$ respectively )

As we have $\implies \angle A B X = \angle B C Y$, the two circumferential equal angles of same circle, the length of the arcs on which these angles stand will be same .

Hence $a r c B Y = a r c A X$ and so chord$A X =$chord $B Y = 4 c m$