the perpendicular from A on BC of triangle ABC intersect on D such that DB=3CD prove that 2AB square=2AC square+BC square

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samrat: the perpendicular from A on BC of triangle ABC intersect on D such that DB=3CD prove that 2AB square=2AC square+BC square

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November 8, 2017 at 4:04pm

Kho Yen Hong:[deqn]AB^2 = AD^2 + BD^2 \\~~~~~~~~~~~~~~~~~~~~= AC^2-CD^2+BD^2 \\~~~~~~~~~~~~~~~~~~~~= AC^2 -CD^2 +9CD^2 \\~~~~~~~~~=AC^2+8CD^2 \\~~~~~~~~~~~~~~~~~= AC^2 + 8(\frac{1}{16}BC^2) \\~~~~~~~~~~~~~~~~~~~~= AC^2 + \frac{1}{2}BC^2 \\\\\ 2AB^2 = 2AC^2 +BC^2[/deqn]
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- November 25, 2018 at 12:35pm

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