Question

please solve this question

Answer 1

In triangle ABY
RAY BX IS BISECTOR OF ANGLE ABY(GIVEN)
AB/BY=AX/XY(BY THE PROPERTY KF AN ANGLE BISECTOR OF A TRIANGLE)

IN TRIANGLE ACY
RAY CX IS BISECTOR OF ANGLE ACY
AC/CY=AX/XY(BY THE PROPERTY OF AN ANGLE BISECTOR OF A TRIANGLE)

AX/XY=AB/BY=AC/CY

AX/XY=5/BY=4/CY

BY THEOREM ON EQUAL RATIOS
EACH RATIO=AX/XY=5+4/BY+CY

AX/XY=9/BC
AX/XY=9/6(SUBSTITUTING THE GIVEN VALUES)
AX/XY =3/2