Question

In triangle abc,ad perpendicular bc,such that ad^2=bd.Cd.Prove that angle a=90 degree

Answer 1

Answer:

Step-by-step explanation:

Given :          In triangle ABC , AD is perpendicular to BC and AD² = BD.DC

To prove :     BAC = 90°

Proof :           in right triangles ∆ADB and ∆ADC

                     So, Pythagoras theorem should be apply ,

                     Then we have ,

                      AB² = AD² + BD² ----------(1)

                      AC²= AD²+ DC² ---------(2)

                     AB² + AC² = 2AD² + BD²+ DC²

                     = 2BD . CD + BD² + CD² [ ∵ given AD² = BD.CD ]

                     = (BD + CD )² = BC²

                    Thus in triangle ABC we have , AB² + AC²= BC²

                    hence triangle ABC is a right triangle right angled at A

                    ∠ BAC = 90°