Question

In a triangle abc, ac > ab, d is the mid point of bc and ae perpendicular to bc. prove that ab² = ad² - bc . de +1/4 bc².

Answer 1

Answer:

In a triangle abc, ac > ab, d is the mid point of bc and ae perpendicular to bc. prove that ab² = ad² - bc . de +1/4 bc².

Answer 2

Answer:

AD is the median of triangle ABC, since D is mid-point of BC.

BD = DC= ....(i)

In right triangle AEB,

(Pythagoras theorem)

AB2 = ()+

(By using Pythagoras theorem for right triangle AED and BE = BD - DE)

AB2 =+....from (i)

AB2 =++ -2

-BC x DE +

Hence proved.