Question

ABC be a triangle with A(1, 3) and internal angle bisector of the angles B and C be y = x and y = -2x respectively. Then

• A. y = 1
• B. y = 2
• C. y = -1
• D. y = -1/2

Answer 1

Answer: (A)

y = 1

Answer 2

The incenter I is the intersection of the angle bisectors $y=x$ and $y=-2x$, which is $I(0,0)$. The reflection of vertex A(1,3) across the angle bisector of B ($y=x$) is $A'(3,1)$. The reflection of vertex A(1,3) across the angle bisector of C ($y=-2x$) is $A''(-3,1)$. Both $A'$ and $A''$ lie on the side BC. The line passing through $(3,1)$ and $(-3,1)$ is $y=1$. Therefore, the equation of side BC is $y=1$.