Question

In A ABC AB. =: AC, seg BD. I seg.: AC. Prove that BD^2-CD^2=2CD*AD

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Answer 1

Given AB=AC, BD⊥AC

From right △ADB,

By pythagorus theorem, AB² = AD² + BD²

⟹ AC² = AD² + BD² (AC = AB)

⟹ (AD + DC)² = AD² + BD²

⟹ AD² + 2.AD.DC + DC² = AD² + BD²

⟹ 2.AD.DC = BD² - CD²

Hence, proved

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