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In triangle PQR, let X be the intersection of the angle bisector of angle P with side QR, and let Y be the foot of the perpendicular from X to line PR.  If PQ = 9, QR = 9, and PR = 9, then compute the length of XY.

 May 20, 2023
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The angle bisector from P bisects QR in X.

\(sin\ 60 ^{\circ}=\dfrac{\overline{XY}}{0.5\cdot \overline{QR}}\\ \overline{XY}=0.5\cdot \overline{QR}\cdot sin\ 60^{\circ}=0.5\cdot 9\cdot sin\ 60^{\circ}\\ \color{blue}\overline{XY}=3.897\)

laugh  !

 May 21, 2023

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