Question

Consider the triangle $ABC$ formed by the points $A(2,4),B(2,6)$ and $C(2+\sqrt{3},5)$. The equation of the internal bisector of $\angle C$ is

• A. $x+y=2$
• B. $x=0$
• C. $y=5$
• D. $x+y=1$

Answer 1

The correct option is C $y=5$

$|AB|=|BC|=|AC|=2$
Hence, the $\Delta ABC$ is equilateral.
The angle bisector will be the same as the median.
The midpoint of $AB$ is $(2,5)$. Hence, the equation of the median from C will be $y=5$.
Hence, option C is correct.