In a ?ABC, A=90, AB=AC and D is a point on BC producd. Prove that DC?-BD?=2AB?AD

Dear student, 

Your question is to be taking as 
In a triangle ABC, ∠A = 90°,  AB=AC and D is a point on AB produced. Prove that DC² - BD²  =2AB AD.

InACDapplying Pythagoras theoremCD2=AC2+AD2CD2=AC2+AB+BD2CD2=AC2+AB2+BD2+2AB.BDCD2-BD2=BC2+2AB AD-ABCD2-BD2=BC2-2AB2+2AB.AD       ....1from ABC,BC2 = AC2+AB2   Pythagoras theoremBC2 = AB2 + AB2    as, AB = ACBC=2ABNow, from 1, CD2-BD2=2AB2-2AB2+2AB.ADCD2-BD2=2AB.AD

  • 0
What are you looking for?