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# Geometry

A triangle $$ABC$$ with sides $$AB = 20; \space BC = 16; \space CA = 4\sqrt{17}$$. Point $$D, \space E, \space F$$ are the midpoints of $$BC, \space CA,\space AB$$ respectively. Point $$P$$ lies on segment $$EF$$, so that $$AP$$ and $$EF$$ are perpendicular to each other. Point $$Q$$ also lies on $$EF$$, so that $$DQ$$ and $$EF$$ are perpendicular to each other. Find the length of $$PQ$$.

Note by Fidel Simanjuntak
1 month, 3 weeks ago

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· 1 month, 3 weeks ago

It should be $$3 \sqrt{\frac{35}{2}}$$, but from the source problem, it's not. But i still sitck to $$3 \sqrt{\frac{35}{2}}$$. · 1 month, 3 weeks ago