Two perpendicular BD and CE are drawn from the vertices B and C respectively on the sides AC and AB of the `Delta ABC`,which intersect each other at the point P. Prove that `AC^(2) + BP^(2) = AB^(2) + CP^(2)`

In Delta ABC, AD_|_ BC . Prove that AB^(2) - BD^(2) =AC^(2) -CD^(2)

In Delta ABC , AD_|_ BC which intersects BC at D. If BD =3 CD , then prove that 2AB^(2) = 2AC^(2)+BC^(2)

Delta ABC is an acute angle triangle inscribed in a circle in a circle .AD is a diameter of the circle . Two perpendiculars BE and CF are drawn from B and C to AC and AB respectively , which intersect each other at the point G . Prove that BDCG is a parallelogram.

If in DeltaABC, AD_|_ BC, then prove that AB^(2) + CD^(2) = AC^(2) + BD^(2)

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.

In DeltaABC , AB = AC. The perpendiculars drawn from B and C to AC and AB respectively, intersect the sides AC and AB at the points E and F respectively. Prove that FE||BC.

In the figure, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(DeltaAOD) = ar(Delta BOC).

ABCD is a rhombus.Prove that AB^(2) + BC^(2) +CD^(2) + DA^(2) = AC^(2) + BD^(2)

ABC is an isosceles triangle right angled at C. Prove that AB^(2) = 2AC^(2) .

In an isosceles right-angled triangle ABC, /_B=90^(@) . The bisector of /_BAC intersects the side BC at the point D. Prove that CD^(2) =2BD^(2)