`D, E, F` are the foot of the perpendiculars from vertices `A, B, C` to sides `BC, CA, AB` respectively, and H is the or the centre of acute angled triangle `ABC,` where `a, b, c` are the sides of triangle `ABC,` then

D , E , F are the foot of the perpendicular from vertices A , B , C to sides B C ,\ C A ,\ A B respectively, and H is the orthocentre of acute angled triangle A B C ; where a , b , c are the sides of triangle A B C , then H is the incentre of triangle D E F A , B ,\ C are excentres of triangle D E F Perimeter of D E F is a cos A+b cos B+c\ cos C Circumradius of triangle D E F is R/2, where R is circumradius of A B C

Let vec a,vec b,vec c form sides BC,CA and AB respectively of a triangle ABC then

D,E,F are the mid points of the sides BC, CA and AB respectively of a triangle ABC . Determine the ratio of the areas of triangle DEF and triangle ABC .

If D,E,F are the mid-point of sides AB,BC and CA respectively of triangle then the ratio of the areas of triangles triangleDEF and ABC is

D, E and F are the mid-points of the sides BC, CA and AB, respectively of and equilateral Delta ABC. Show that Delta DEF is also an equilateral triangle.

D, E and F are the mid-points of the sides BC, CA and AB, respectively of an equilateral Delta ABC. Show that Delta DEF is also an equilateral triangle.