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

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

1.	In a triangle ABC , AD perpendicular to BC and AD²= BD.CD . Prove that ABC is a right triangle .
Answer» 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^2Thus in triangle ABCAB^2 + AC^2 = BC^2Hence triangle ABC is a right angle triangle Angled at A. Angle BAC = 90