perplexus.info :: Geometry : Right triangle projections

Right triangle projections (Posted on 2025-04-30)

Let KDO be a triangle with right angle at K. Let the projection of K onto DO be M. Given that KD*KM*KO=324, compute DM*MO*DO.

No Solution Yet Submitted by Danish Ahmed Khan

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Solution

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The lengths given all fit the mean proportionals in a right triangle:

KM^2 = DM*MO

KO^2 = MO*DO

KD^2 = DM*DO

The product of these three equations is then

KM^2*KO^2*KD^2 = DM^2*MO^2*DO^2

KD*KM*KO = DM*MO*DO = 324

Posted by Jer on 2025-05-01 10:13:07

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