# Article

MSC: 51M04, 97G40
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Summary:
This article presents the following simple property of a general triangle \$ABC\$: Let \$D\$ be an arbitrary point and \$A_0\$, \$B_0\$, \$C_0\$ the feet of the perpendiculars from \$D\$ on the (possibly extended) sides \$BC\$, \$CA\$, \$AB\$, respectively. Then \[ |{AC}_0|^2 + |{BA}_0|^2 + |{CB}_0|^2 = |{C_0B}|^2 + |{A_0C}|^2 + |{B_0A}|^2. \] This statement is a proper generalization of the Pythagorean theorem. Surprisingly, it does not appear in textbooks or other publications.
References:
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