In a triangle ABC, AD is the median drawn on the side BC is produced to E such that `AD = ED` prove that ABEC is a parallelogram.

In triangle ABC, D is the mid point of side BC . If AD is perpendicular to AC . then prove that cosA cosC =(2(c^2-a^2))/(3ca)

In an equilateral triangle ABC, D is a point on side BC such that BD = (1)/(3) BC. Prove that 9 AD^(2) = 7 AB^(2) .

I is the incentre of Delta ABC , Produced AI bisects BC at D. Prove that Delta ABC is isosceles.

In an isosceles triangle ABC with AB = AC, D and E are points on BC such that BE = CD. Show that AD = AE.

Delta ABC is an acute angle triangle inscribed in a circle in a circle .AD is a diameter of the circle . Two perpendiculars BE and CF are drawn from B and C to AC and AB respectively , which intersect each other at the point G . Prove that BDCG is a parallelogram.

In Delta ABC ,AD is a perpendicular drawn from A to the side BC. If AD^(2)=BD . CD , then prove that the triangle is a right-angled triangle.

Delta ABC is an equilateral triangle . D is a point on the side BC such that BD = (1)/(3) BC . Prove that 7 AB^(2) = 9AD^(2)

P is a point on the median AD of the Delta ABC . Prove that area of Delta APB = area of Delta APC .

In an equiliteral triangle ABC, if AD bot BC , then___