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.
+15000 Compute the length of XY.
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\(\overline {XY}=\overline{PR}\cdot cos\ 30^{\circ}=\sqrt{\overline{PR}\ ^2-(\frac{\overline{PR}}{2})^2}\\ \overline{XY}=9\cdot cos\ 30^{\circ}=\sqrt{9^2-(\frac{9}{2})^2}=\color{blue}7.794\)
The length of \(\overline{XY}\) is 7.794.
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