Let ABC be a triangle such that AB=BC. Let F be midpoint of AB and X be a poin on BC such that FX is perpendicular to AB. If BX =3XC then the ratio BC/AC equals

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

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

Let ABC be an acute-angled triangle and let D be the midpoint of BC. If AB = AD, then tan(B)/tan(C) equals

AB is a straight line, C and D are points on the same side of AB such that AC is perpendicular to AB and DB is perpendicular to AB. Let AD and BC meet at E. What is (AE)/(AD) + (DE)/(BC) equal to ?

ABC is a triangle with AB= AC and D is a point on AC such that BC^(2)= AC xx CD . Prove that BD= BC.

In Delta ABC, AB = AC. D , E and F are mid-points of the sides BC, CA and AB respectively . Show that : AD is perpendicular to EF.

Let ABC be an isosceles triangle with AB=AC and let D,E,F be the mid-points of BC,CA and AB respectively.Show that AD perp FE and AD is bisected by FE .