Question

solution plz........​

Answer 1

Step-by-step explanation:

$\because$ BX & CX are bisectors of $\angle B \: \& \:\angle C$ respectively.

$\therefore$ By Angle Bisector Theorem:

$\frac{AX}{XY} =\frac{AB} {BY} .... (1)$

&

$\frac{AX}{XY} =\frac{AC}{CY}.... (2)\\\\</p><p>$

From equations (1) & (2)

$\frac{AX}{XY} =\frac{AB}{BY}=\frac{AC}{CY}\\\\</p><p>$

$\therefore Let\: \frac{AX}{XY} =\frac{AB}{BY}=\frac{AC}{CY}=k\\\\</p><p> \therefore k=\frac{AB}{BY}=\frac{AC}{CY}\\\\</p><p> \therefore k=\frac{AB+AC}{BY+CY}\\(By\: Theorem \: on \: equal \: ratios) \\\\</p><p> \therefore k=\frac{AB+AC}{BC}... (\because BY+CY= BC) \\\\</p><p>\huge \orange {\boxed {\therefore \frac{AX}{XY} = \frac{AB+AC}{BC}}}$

Hence Proved