Question

ABC is a triangle, D is the mid-point on side BC.

Given, AB=5 cm, AC=5 cm and BD=3 cm
Find the value of AD.

Answer 1

From Apollonius's theorem, we can say



$A{B}^2+A{C}^2=2(B{D}^2+A{D}^2)$
Substituting the values we get,
$5^2+5^2=2(3^2+A{D}^2)25+25=2(9+A{D}^2)A{D}^2+9=25\Rightarrow A{D}^2=16\Rightarrow AD=4cm$