Question

in exercises 5 and 6, the angle bisectors of △xyz intersect at point p and are shown in red. find the indicated measure.

1. pb
2. hp

Explanation:

Step1: Recall the property of the in - center of a triangle

The in - center of a triangle (the point of intersection of the angle bisectors) is equidistant from all the sides of the triangle.

Step2: Use the equidistant property

Since \(P\) is the in - center of \(\triangle XYZ\) (intersection of angle bisectors), \(PA = PB=PC\). Given \(PC = 9\), by the property that the in - center is equidistant from the sides of the triangle.

Answer:

\(PB = 9\)