In triangle $XYZ,$ $M$ is the midpoint of $\overline{XY}.$ Let $D$ be the point on $\overline{YZ}$ such that $\overline{XD}$ bisects $\angle YXZ,$ and let the perpendicular bisector of $\overline{XY}$ intersect $\overline{XD}$ at $P.$ If $XY = 36$ and $MP = 9,$ then find the distance from $P$ to line $XZ.$

Answer 1

I will delete all that fancy code, which does nothing on this site.

In triangle XYZ, M is the midpoint of XY. Let D be the point on YZ such that XD bisects angle YXZ, and let the perpendicular bisector of XY intersect XD at P. If XY = 36 and MP = 9, then find the distance from P to line XZ.

Lots of wording for a simple problem.
Let the perpendicular from P to XZ meet XZ at Q
After filling in all the details, it is easy to see that triangle MPX and triangle QPX are congruent which makes PQ equal to 9.

Answer 2

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