D,E,F are the mid-point of the three sides of a triangle and if P be the pedal-point of the perpendicular drawn fron one of its vertices to its opposite side, then prove that D,P,E and F are concylic.

The lengths of three sides of a triangle are 5cm, 12cm and 13 cm. Then find the length of the perpendicular drawn from the opposite vertex of the side of length 13 cm to that side.

If D is the mid point of side BC of a triangle ABCand AD is perpendicular to BC, then

Prove analytically that in any triangle the perpendiculars drawn from the vertices upon the opposite sides are concurrent.

If (4,3) , (-2,7) and (0,11) are the coordinates of the mid -points of the sides of a triangle , find the coordinates of its vertices .

If the midpoints of the sides of a triangle are (2,1),(-1,-3),a n d(4,5), then find the coordinates of its vertices.

D, E and F are the mid-points of the sides AB, AC and BC of the DeltaABC. Prove that DE and AF bisects each other.

D, E and F are the mid-points of the sides AB, BC and CA of the DeltaABC . Prove that DeltaDEF=1/4DeltaABC .

The coordinates of one of the vertices of a triangle is (2,0) and the coordinates of the mid-points of its opposite side is (5,3) . Find the length of the median.

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