In `square ABCD`, AB||CD. Diagonals AC and BD intersect each other at point P. Prove that `A(triangle ABP)`:`A(triangle CPD)`=`(AB)^2:(CD)^2`.

In square ABCD , seg AD|| seg BC. Diagonal AC and digonal BD intersect each other in point P. Then show that (AP)/(PD)=(PC)/(BP) .

In squareABCD , side BC|| side AD . Digonals AC and BD intersect each other at P . If AP=(1)/(3)AC then prove DP=(1)/(2)BP .

square ABCD is a parallelogram.Side BC intersects circle at point P.Prove that DC=DP

square ABCD is a trapezium in which AB||DC and its diagonals intersect each other at point O. Show that AO:BO = CO:DO.

In triangle ABC , points D and E are on sides BC and AB such that AD and CE intersect at point P. CE_|_AB , AD_|_BC . Prove that triangle AEP~triangle CDP

In triangle ABC , points D and E are on sides BC and AB such that AD and CE intersect at point P. CE_|_AB , AD_|_BC . Prove that triangle AEP~triangle ADB

In the figure, seg AC and seg BD intersect each other in point P and (AP)/(CP)=(BP)/(DP) . Prove that DeltaABP~DeltaCDP .

Line AC and line BD intersect each other in the point P. mangleAPD=47^@ . Find the measures of angle APB, angleBPC, angleCPD .

In trapezium ABCD side AB|| side DC, diagonals AC and BD intersect In point O. If AB=20, DC=6, OB=15 then find OD.

Line PQ is a tangent to the circle at point A, arc AB~=arc AC . Prove that triangle ABC is isosceles triangle.