Diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at the point ‘O’. Using the criterion of similarity for two triangles, show that ` (OA)/(OC) = (OB)/(OD)` .

Diagonals of a trapezium ABCD with AB || DC, intersect each other at the point ‘O’. If AB = 2CD, find the ratio of areas of triangles AOB and COD.

In the figure, diagonals AC and BD of a trapezium ABCD with AB || DC intersect each other at O. Prove that ar(DeltaAOD) = ar(Delta BOC).

Two chords AB and CD of a circle with centre O intersect each other at the point P. If ∠AOD =20° and ∠BOC = 30°, then ∠BPC is equal to?

The diagonals AC and BD of a quadrilateral ABCD intersects each other at O such that DeltaAOD=DeltaBOC . Prove that ABCD is trapezium.

If two chords AB and CD of a circle with centre O, when produce intersect each other at the point P, then prove angleAOC-angleBOD = 2angleBPC .

Two chords AB and CD of the circle with centre at O intersect each other at an internal point P of the centre. Prove that angle AOD+ angle BOC=2 angle BPC

Two chords AC and BD of a circle intersect each other at the point O. If two tangents drawn at the points A and B intersect each other at the point P and two tangents drawn at the points C and D intersect at the point Q, prove that angle P+ angle Q =2 angle BOC. [GP-X]

The two medians BE and CF of DeltaABC intersect each other at the point G and if the line segment FE intersects the line segment AG at the point O , then prove that AO=3OG .

If two chords AB and CD of a circle with centre, O, when producd intersect each other at the point P, prove that angle AOC- angle BOD=2 angle BPC .