Pythagorean theorem and orthocenterPoint H is the orthocenter of △ A B C. Let AD and CM be the altitudes. Show that B M 2 − B D 2 = H D 2 − H M 2 .By Pythagorean theorem: 1) △ △ B C M → B M 2 = B C 2 − C M 2 and 2) △ A B D → B D 2 − A B 2 − A D 2 How to approach the problem further?

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Pythagorean theorem and orthocenterPoint H is the orthocenter of   △  A  B  C. Let AD and CM be the altitudes. Show that   B      M    2    −  B      D    2    =  H      D    2    −  H      M    2  .By Pythagorean theorem: 1) △  △  B  C  M  →  B      M    2    =  B      C    2    −  C      M    2   and 2)   △  A  B  D  →  B      D    2    −  A      B    2    −  A      D    2   How to approach the problem further?

victorollaa5 · Accepted Answer

Write Pytagorean theorem in right triangles which includes also the point H, say HCD and HAM.Better, try HBM and HBD.

Pythagorean theorem and orthocenter Point H is the orthocenter of <mi mathvariant="normal">&#x25

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