Let `A B C` be a triangle with `A B=A Cdot` If `D` is the midpoint of `B C ,E` is the foot of the perpendicular drawn from `D` to `A C ,a n dF` is the midpoint of `D E ,` then prove that `A F` is perpendicular to `B Edot`

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.

A B C is a triangle in which D is the mid-point of B C and E is the mid-point of A Ddot Prove that area of B E D=1/4a r e aof A B Cdot GIVEN : A A B C ,D is the mid-point of B C and E is the mid-point of the median A Ddot TO PROVE : a r( B E D)=1/4a r( A B C)dot

A B C is a triangle. D is the mid point of B Cdot If A D is perpendicular to A C , then prove that cos A\ dotcos C=(2(c^2-a^2))/(3a c) .

Let A B C be an isosceles triangle with A B=A C and let D ,\ E ,\ F be the mid points of B C ,\ C A\ a n d\ A B respectively. Show that A D_|_F E\ a n d\ A D is bisected by F E

Let AB be a line segment with midpoint C, and D be the midpoint of AC. Let C_1 be the circle with diameter AB and C_2 be the circle with diameter AC. Let E be a point on C_1 such that EC is perpendicular to AB. Let f be a point on C_2 such that DF is perpendicular to AB. Then, the value of sinangleFEC is

A B C is a triangle in which D is the mid-point of B C ,\ E\ a n d\ F are mid-points of D C\ a n d\ A E respectively. If area of A B C is 16\ c m^2, find the area of D E F

B M\ a n d\ C N are perpendicular to a line passing through the vertex A of a triangle A B Cdot If L is the mid-point of B C , prove that L M=L N

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

Let A B C be an isosceles triangle in which A B=A Cdot If D ,\ E ,\ F be the mid-points of the sides B C ,\ C A\ a n d\ A B respectively, show that the segemtn A D\ a n d\ E F bisect each other at right angles.

In Figure, B M a n d D N are both perpendiculars to the segments A C a n d B M=D N . Prove that A C bisects B D