Points P, Q and R lie on sides BC, CA and AB respectively of triangle ABC such that PQ || AB and QR || BC, prove that RP II CA.

D and E are points on sides AB and AC respectively of DeltaABC such that ar (DBC) = ar (EBC). Prove that DE II BC .

If D, E and F are three points on the sides BC, CA and AB, respectively, of a triangle ABC such that the lines AD, BE and CF are concurrent, then show that " "(BD)/(CD)*(CE)/(AE)*(AF)/(BF)=1

If P,Q and R are the mid-point of the side BC,CA and AB of a triangle and AD is the perpendicular form A and BC, prove that P,Q and D are concylic.

AL, BM and CN are perpendicular from angular points of a triangle ABC on the opposite sides BC, CA and AB respectively. Delta is the area of triangle ABC, (r ) and R are the inradius and circumradius. Radius is the circum circle of Delta LMN is

AL, BM and CN are perpendicular from angular points of a triangle ABC on the opposite sides BC, CA and AB respectively. Delta is the area of triangle ABC, (r ) and R are the inradius and circumradius. If perimeters of DeltaLMN and Delta ABC an lamda and mu, then the value of (lamda)/(mu) is

AL, BM and CN are perpendicular from angular points of a triangle ABC on the opposite sides BC, CA and AB respectively. Delta is the area of triangle ABC, (r ) and R are the inradius and circumradius. If area of Delta LMN is Delta ', then the value of (Delta')/(Delta) is

In the fig D,E and F are the mid points of the sides BC,CA and AB respectively of triangleABC . If BE and DF intersect at X while CF and DE ntersect at Y. prove that XY=1/4BC

D,E and F are mid-points of the sides BC, CA and AB respectively of triangleABC . Prove that ar(||gmBDEF)= 1/2 ar (triangleABC)

In a triangle, P, Q and R are mid-points of sides BC, CA and AB respectively. If AC = 21 cm, BC = 29 cm and AB = 30 cm, find the perimeter of the quadrilateral ARPQ.

D,E,F are the middle points of the sides [BC],[CA],[AB] respectively of a triangle ABC. Show that : FE is parallel to BC and half of its length.