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In triangle PQR, M is the midpoint of PQ. Let X be the point on QR such that PX bisects angle QPR, and let the perpendicular bisector of PQ intersect PX (AX incorrect) at Y. If PQ = 36, PR = 22, QR = 26, and MY = 8, then find the area of triangle PQR

 Feb 27, 2024
edited by asinus  Feb 28, 2024
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Hello blackpanther!

I have corrected AX on PX.

 

\(\frac{\angle YPM}{2}=atan\ \frac{8}{18}=23.962^\circ\\ \angle RPM=47.925^\circ\\ h_{via\ PQ}=22\cdot sin\ \angle RPM=22\cdot sin\ 47.925^\circ\\ h_{via PQ}=16.32\\ A_{\triangle PQR}=\frac{1}{2}\cdot 36\cdot 16.32\\ \color{blue}A_{\triangle PQR}=293.76\)

 

laugh !

 Feb 28, 2024

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