Right Triangle In Triangle

Geometry Level 5

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

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

Note:

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

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

The diagram may not be drawn to scale.

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