Question

in a equilateral triangle abc..,d is a point on dC such that bd =1/3 bc.prove that 9ad²=7ab²​

Answer 1

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.