P is the incenter of ΔXYZ. If PY = 35 and JY = 28, find LP.

REMEMBER = PJ^2 is known as PJ raise to 2

Given that the point P is an incenter of ΔXYZ. Also, PY = 35 and JY = 28.

We are to find the length of LP.

Since PJ is perpendicular to teh side YZ, so the triangle PJY will be a right-angled triangle with PY as the hypotenuse.

Using Pythagoras theorem in triangle PJY, we have

PY^2 = PJ^2 + YJ^2

= PJ^2 = PY^2 - YJ^2

= PJ^2 = 35^2 - 28^2

= PJ^2 = 441

= PJ^2 = 21

Since the distance from the incenter of a triangle to all the three sides are equal, so we get

LP = PJ = 21 units.

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