Question

Let ABC be a triangle with AB = AC . If D is mid point of BC, the foot of the perpendicular drawn from D to AC and F the mid point of DE. Prove that AF is perpendicular to BE.

Answer 1

Let BC be taken as x-axis with origin at D, the mid point of BC, and DA will be y-axis.

Given, AB = AC

Let BC = 2a, then the coordinates of B and C are (- a,0) and (a, 0) let A(0, h).

Then, equation of AC is