In `triangle` ABC, the bisectors of `angle`B and `angle` C intersect at I. A line drawn through I and parallel to BC intersects AB at P and AC at Q. Prove that PQ = BP + CQ.

ABCD is a parallelogram whose diagonals AC and BD intersect at O. A line through O intersects AB at P and DC at Q. Prove that ar (Delta POA) =" ar "(Delta QOC) .

ABCD is a trapezium with AB||DC. A line parallel to AC intersects AB at X and BC at Y. Prove that ar( Delta ADX) = ar( Delta ACY).

In o+ABC,AB=AC, and the bisectors of angles B and C intersect at point O. Prove that BO=CO and the ray AO is the bisector of angles BAC.

In ABC,AB=AC, and the bisectors of angles B and C intersect at point O .Prove that BO=CO and the ray AO is the bisector of angle BAC

If in a Delta ABC angle bisectors of exterior angle angle B and angle C intersect at P angle BPC = 40^(@) find angle A

In a Delta ABC , angle bisector of interior angle B and exterior angle C intersect at P . If angle A=70^(@) . Find angle BPC .

Internal bisector of /_A of triangle ABC meets side BC at D. A line drawn through D perpendicular to AD intersects the side AC at E and the side AB at F. If a, b, c represent sides of DeltaABC, then

In the triangle ABC, the base BC is trisected at D and E. The line through D, parallel to AB, meets AC at F and the line through E parallel to AC meets AB at G. Let EG and DF intersect at H. What is the ratio of the sum of the area of parallelogram AGHF and the area of the triangle DHE to the area of the triangle ABC ?

P is a point on the bisector of an angle /_ABC. If the line through P parallel to AB meets BC at Q, prove that triangle BPQ is isosceles.