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In triangle $PQR,$ let $X$ be the intersection of the angle bisector of $\angle P$ with side $\overline{QR}$, and let $Y$ be the foot of the perpendicular from $X$ to side $\overline{PR}$.  If $PQ = 8,$ $QR = 5,$ and $PR = 1,$ then compute the length of $\overline{XY}$.

 Jul 31, 2024
 #1
avatar+1926 
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mmm...let's note something really quickly. 

In the problem, it said that

\(QR + PR < PQ \)

 

However, it said that PQR is a triangle, but this violates the Triangle Inequality Theorem.

 

So this problem is invalid. 

 

thanks! :)

 Jul 31, 2024
edited by NotThatSmart  Jul 31, 2024

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