`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 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 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 .

squareLMNO is a square. Diagonlas LN and MO intersect each other at point S. Find angleSMN

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.

In the adjoining figure, two circles intersect each other at points A and E. Their common secant through E intersects the circle at points B and D. The tangents of the circles at point B and D intersect each other at point C. Prove that square ABCD is cyclic.

Diagonals SU and TV of rhombus STUV intersect each other at point W. Find angleSWT .

square ABCD is a parallelogram. Point E is on side BC. Line DE intersects Ray AB in point T. Prove that DE xx BE=CE xx TE .

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

In the adjoining figure, seg YZ and seg XT are altitudes of triangle WXY which intersect each other at point P. Prove that square WZPT is a cyclic quadrilateral.

In the adjoining figure, seg YZ and seg XT are altitudes of triangle WXY which intersect each other at point P. Prove that: Points X, Z, T and Y are concyclic points.