Question

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

Answer 1

Explanation:

Hope it helps

Thank you

Answer 2

Explanation:

Given: AB = BC = CA - (1) ( abc is equilateral triangle)

const. : draw AE perpendicular to BC

proof: BD = 1/3 BC - (2) (given)

BE = EC = 1/2 BC - (3) ( altitude AE divides BC in half)

DE = BE - BD

= 1/2BC - 1/3BC. (from 2 and 3)

= 3BC - 2BC/6

= BC/6 (4)

in AEB, by Pythagoras theorem

AB^2 = BE^2 + AE^2 (5)

In AED, by p.t.

AD^2 = DE^2 + AE^2. (6)

from 5 and 6

AB^2 - AD^2 = BE^2 - DE^2

.........................= (1/2BC)^2 - (BC/6)^2. (From 3 and 4)

…………………….=now do by yourself