Question

In ΔABC, AB=AC and BD perpendicular to AC, Prove that BD^2 + CD^2=2AC.CD

Answer 1

in triangle ABD,

pythagoras theorem,

AB²=BD²+DA²

AC²=BD²+DA² (AB=AC)

(AD+DC)²=BD²+DA²

AD²+DC²+2×AD×DC=BD²+DA²

thus, 2(CD)(AD)=BD²-CD²

hope it helped yeh..