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.

AD is the median on BC. Find the coordinates of the point D

In the figure, ABC is a triangle in which AB= AC. Points D and E are points on the side AB and AC respectively such that AD=AE. Show that points B, C, E and D lie on a same circle.

If D is the midpoint of the side BC of a triangle ABC, prove that vec(AB)+vec(AC)=2vec(AD)

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

From a point O inside a triangle ABC, perpendiculars OD, OE and OF are drawn to the sides BC, CA and AB, respectively. Prove that the perpendiculars from A, B and C to the sides EF, FD and DE are concurrent

The median AD of the triangle ABC is bisected at E and BE meets AC at F. Find AF:FC.

In Delta ABC , AB = AC and BC = 6cm, D is a point on the side AC such that AD = 5cm and CD = 4cm, show that Delta BCD ~ Delta ABC and hence find DB .

ABC is triangle. D is the middle point of BC. If AD is perendicular to AC, then prove that cosAcosC=(2(c^(2)-a^(2)))/(3ac)

In triangle ABC, if a = 2 and bc = 9, then prove that R = 9//2Delta