# Right Triangle In Triangle

Geometry Level 5

In the figure above, $$\Delta ABC$$ is a triangle. $$\overline { AD }$$ is the angle bisector of $$\angle BAC$$. Also $$\angle BDA={ 90 }^{\circ}$$ and $$M$$ is a point on $$\overline {BC}$$ so that $$|\overline { BM } |=|\overline { MC } |$$.

Given that $$|\overline {AB}|=17$$ and $$|\overline {AC}|=61$$, find $$|\overline {DM} |$$.

Note:

$$|\overline {DM}|$$ refers to the length of line segment DM.

$$\overline {DM}$$ refers to the line segment DM.

The diagram may not be drawn to scale.

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