In an equilateral triangle ABC, D is a point on side BC such that BC. Prove that 9AD2 = 7AB2.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

Draw AP BC.

BD =

Since ABC is equilateral and AP BC,

BP = PC = BC = AB

Using Pythagoras theorem in ABP,

AP2 + BP2 = AB2

AP2 = AB2 - BP2 = AB2 - = … (1)

Using Pythagoras theorem in ADP,

AD2 = AP2 + DP2

= AB2 + (BP - BD)2

= AB2 +

=

36AD2 = 28AB2

9AD2 = 7AB2

Hence, proved.

Answered by  | 4th Jun, 2014, 03:23: PM