Question

In an equilateral triangle ABC, D is a point on side BC such that BD =
-
BC. Find the value of AD2​

Answer 1

Answer:

It is given that D is a point on BC such that BD=CD

Hence, D is the mid-point of BC

Construction-Join AD

Now median AD divides triangle into two right-angled Δ ABD & ACD

Since ABC is an equilateral Δ, AB=AC=BC

Now in ΔABD,

AB²= AD²+BD²                

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

In ΔACD,

AC²=AD²+ CD²

AD²= AC²- CD²                     ...................(2)

From (1) & (2),

AD²= AB²-BD²=AC²-CD²

        = AB²+CD²=AC²+BD²

       

Step-by-ep explanation: