Question

in triangle abc ad is perpendicular to bc such that ad^2 =bd×cd prove that abc is right angled at a

Answer 1

In the $\Delta ABC$, AD is perpendicular to BC and $AD^2=BD*CD$.

From the attached figure,

$AB^2=AD^2+BD^2\\ AC^2=AD^2+BC^2$

Adding the above 2 equations, we get

$AB^2+AC^2=2AD^2+BD^2+DC^2\\ AB^2+AC^2=2*BD*DC+BD^2+DC^2\\ AB^2+AC^2=(BD+DC)^2\\ AB^2+AC^2=BC^2$

$AB^2+AC^2=BC^2$ is nothing but Pythagoras theorem. That ijs

$\Delta ABC$ is right angled at A.

Answer 2

Answer:

Check your answer please