Question

Find the measure of PB if point P is the incenter of triangle AEC. Enter your answer as a number rounded to the nearest tenth.

Answer 1

EXPLANATION

If the point P is the incenter of the triangle, then the Incenter Theorem determine that the incenter formed by angle bisectors is EQUIDISTANT frmo the sides of the triangle, wich means that all three perpendicular distances from the incenter are the same length.

Here we have side EP represents 2/3 of the total length, so side PB will be 1/3 of the total length:

EP---------------> 2/3

PB--------------> 1/3

The relationship will be:

EP/2/3 = PB/1/3

We have that EP=14.9, so replacing:

`(14.9)/((2)/(3))=(PB)/((1)/(3))`

Multiplying both sides by 1/3:

`(1)/(3)\cdot(14.9)/((2)/(3))=PB`

Multiplying:

`(149)/(20)=PB`

Switching:

PB = 149/20 = 7.45

Answer: the measure of PB is equal to 7.4 (rounded to the nearest tenth).