D,E,F are the mid-point of the sides of a triangle and if P the foot of the perpendicular drawn from any vertex of the triangle to its opposite side, then prove that D,P,E,F are concylic.

Show that the perpendicular from the vertices of a triangle to the opposites sides are concurrent .

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

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.

The two sides adjacent to the right-angled triangle are 9 cm and 12 cm. Find the length of the perpendicular drawn from the vertex to the hypotenuse.

The sides of a triangle are 15 cm, 20 cm and 25 cm. Find the perpenducular distance of its greatest sides from its oppsite vertex.

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

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

D, E and F are the mid-points of the sides of BC, CA and AB of the DeltaABC . If DeltaABC=16Sq.cm., then the area of the trapezium FBCE is-

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 is the mid-point of BC of DeltaABC . E and O are the mid-points of BD and AE respectively. Then the area of the triangle BOE is-