P is a point on AB of a quadrilateral ABCD. If PQ drawn parallel to BC cuts AC at Q and QR drawn parallel to AD cuts CD at R then prove that `DR : RC = AP : PB`.

ABC is a triangle of area 256 cm^2 . XY is drawn parallel to BC meeting AB at X and AC at Y. If AX:XB= 3:5 . Find the area of /_\AXY .

A quadrilateral ABCD is drawn to tu circumscribe a circle. Prove that AB+CD=AD+BC .

Line segment drawn parallel to the base BC of ∆ABC cuts AB and AC at D and E respectively. DP , AL and EQ are perpendicular on BC. Prove that LP : PB = LQ : QC .

A line segment drawn parallel to the base BC of ∆ABC intersects AB and AC at X and Y respectively. If AB = 4 , AC = 3 and AY = 1.8 then prove that BX= 1.6 .

A line drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. If AQ : QC = 7: 4 and AB = 8.8 then determine AP and PB.

AB and CD two parallel sides of trapezium ABCD where AB=2 CD . AC and BD intersects at X. prove that AX=2/3AC .

M is the mid point of the side CD of the parallelogram ABCD. The line BM is drawn intersecting AC in L and AD produced at E.Prove that(ii) EL = 2BL

D and E are respectively the point on the sides AB and AC of a trinagle ABC such that DE|\|BC . Through the point E a line parallel to CD is drawn which cut AB at the point F then show that AD^2=ABxxAF

A line PQ drawn parallel to the base BC of ∆ABC intersects AB and AC at P and Q respectively. AP = 1/3 PB then determine (area of ABC)/(area of APQ)

Two triangles ABC and DBC are in the same side of the common base BC. Lines drawn parallel to BA and BD from any point E on BC intersect AC and DC at the points P and Q respectively. Show that PQ is parallel to AD.