In a ABC, angle A=90, CA=AB and D I'd the midpoint on AB produced. Prove that DCsquare - BD square=2AB*AD
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In a triangle ABC,∠A = 90°, CA=AB and D is a point on AB produced.
According to Pythagoras theorem, DC2 = AD2 + AC2
DC² - BD² = (AD2 + AC2) - (AD - AB)2
= (AD2 + AC2) - (AD2 + AB2 - 2 AD . AB)
= AD2 + AC2 - AD2 - AB2 + 2 AD . AB
= AC2 - AB2 + 2 AD . AB
= AC2 - AC2 + 2 AD . AB [Since AC = AB]
= 2 AD . AB
Hence proved.
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