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6. In an isosceles triangle ABC with AB AC, BD is a perpendicular from B to the side AC.Prove that BD CD 2CD AD. |
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Answer» UsingPythagoras theorem: AD² + BD² = AC² (= AB²) --- (1) CD² + BD² = BC² ------- (2) (2)- 2 * (1) =>=> CD² - BD² = BC² - 2AC² + 2 AD²=> = BC² - 2(AD +CD)² + 2 AD²=> = BC² - 2 CD² - 4 AD * CD=> = BD² + CD² - 2 CD² -4 AD * CD=> = BD² - CD² - 4 AD * CDSimplify to get BD² - CD² = 2 AD * CD l |
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