AB and BD are two parallel sides of trapezium ABCD. if the diagonals AC and BD meet at O, then prove that `(AO)/(OC) = (BO)/(OD)`.

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

In trapezium ABCD , AB||DC and AC and BD diagonal intersect at the point E. Prove that (EA)/(EC)=(EB)/(ED).

In a trapezium ABCD, the side AB is parallel to DC and the diagonals AC and BD meet at X. Prove that XA*XD = XB*XC .

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

If BD and CE are two altitudes of triangleABC ,prove that (CA)/(AB)=(CE)/(DB)

ABC and DBC are two right angled triangles with common hypotenuse BC with their sides AC and BD intersecting at P. Prove that: AP×PC=DP×PB .

Of the trapezium ABCD, AB||DC and DC = 2AB. If the line segment EF drawn parallel to AB meets AD and BC at the points Fand E respectively so that (BE)/(EC)=3/4 and the diagonal DB meets EF at the points G, prove that 7FE=11AB

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.

E is any point on the side BC of the parallelogram ABCD. AE intersects the diagonal BD at point F. Prove that DF×EF=FB×FA .

AC and BD are two perpendicular diameters of a circle ABCD. If AC=16 cm calculate the area and the perimeter of the shaded part.