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In a triangle ABC , AD …

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In a triangle ABC , AD perpendicular to BC and AD²= BD.CD . Prove that ABC is a right triangle .

Posted by :) ** 5 years, 10 months ago

CBSE > Class 10 > Mathematics

1 answers

Kirandeep Kaur 5 years, 10 months ago

In triangle ADB and ADC Using pythagoras theorem: AB^2 = AD^2+BD^2....... (1) AC^2 = AD^2 + DC ^2......(2) Now, AB^2 +AC^2 = 2AD^2 +BD^2 +DC^2 = 2 BD. CD + BD^2 +CD^2 (Given that AD^2=BD.CD) (BD + CD)^2 = BC^2 Thus in triangle ABC AB^2 + AC^2 = BC^2 Hence triangle ABC is a right angle triangle Angled at A. Angle BAC = 90

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CBSE > Class 10 > Mathematics