ABC is an acute-angled triangle .AP is the diameter of the circumcircle of the triangle ABC, EB and CF are perpendiculars on AC and AB respectiely and they intersect each other at the point other at the point Q. Prove that BPCQ is a parallelogram.

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.

ABC is a triangle in which BE and CF are perpendiculars to AC and AB respectively. If BE=CF, prove that triangleABC is isosceles.

In two chords AB and CD intersect each AB and CD intersect each other at the point P. Prove that Delta APC ~ Delta DPB

B is a vertex of the isosceles triangle ABC. D and E are the mid-points of AB and AC. If BE and CD intersects each other at F prove that DeltaBDE=3DeltaDEF .

If in a triangle ABC, BE and CF are two medians perpendicular to each other and if AB=19 cm and AC=22 cm then the length of BC is

In Delta ABC, D,E and F are mid-point of sides AB ,BC and AC respectively , Prove that AE and DF bisect each other.

The perpendicular bisectors of the three side of an acute triangle intersect each other

If the radius of the circumcircle of the isosceles triangle ABC is equal to AB(=AC), then the angle A is equal to-

If the radius of the circumcircle of the isosceles triangle ABC is equal to AB(=AC), then the angle A is equal to-