`A B C` is a triangle and `D` is the mid-point of `B C` . The perpendiculars from `D` to `A B` and `A C` are equal. Prove that the triangle is isosceles.

ABC is a triangle and D is the mid-point of BC .The perpendiculars from D to AB and AC are equal.Prove that the triangle is isosceles.

If cos B=(sin A)/(2sin C) then prove that the triangle is isosceles.

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) .

If in a Delta ABC, c(a+b) cos B//2 = b(a+c) cos C//2 , prove that the triangle is isosceles.

The bisectors of the angles B and C of a triangle ABC, meet the opposite sides in D and E respectively.If DE|BC, prove that the triangle is isosceles.

If O is a point in space, A B C is a triangle and D , E , F are the mid-points of the sides B C ,C A and A B respectively of the triangle, prove that vec O A + vec O B+ vec O C= vec O D+ vec O E+ vec O Fdot

In a Delta ABC if (a+b)cos((B)/(2))=b(a+c)cos((C)/(2)) then prove that the triangle ABC is isosceles.

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

In right triangle A B C , right angle at C , M is the mid-point of the hypotenuse A Bdot C is jointed to M and produced to a point D such that D M=C Ddot Point D is joined to point Bdot Show that A M C~= B M D (ii) /_D B C=/_A C B D B C~= A C B (iii) C M=1/2A B