Question

Which of the following must be true if P is the incenter of triangle ABC?

A) PA = PB
B) PX = PY
C) YA = YB
D) AX = BZ

Answer 1

If P is the incenter of triangle ABC, the correct statement would be A) PA = PB.

Step-by-step explanation:

If P is the incenter of triangle ABC, the correct statement would be A) PA = PB.

By definition, the incenter of a triangle is the point where the angle bisectors of the triangle intersect. The angle bisectors divide the sides of the triangle into two equal parts. In this case, the angle bisectors divide sides AB and AC into two equal parts, creating equal segments from P to A and P to B respectively. Therefore, statement A) PA = PB must be true.