Question

1. If DC is an angle bisector, what is the

measure of DCB?

2. Without constructing, will the incenter lie
inside or outside this triangle? Why or why
not?

Answer 1

1.

∠DCB is the half of the measure of ∠ACB as the angle bisector DC cut it in two equal parts.

• m∠DCB = 1/2m∠ACB
• m∠DCB = 1/2(101.31°) = 50.655°

2.

The incenter is the intersection of the angle bisectors.

All three angle bisectors lie inside the triangle, hence the incenter is always inside.