In trapezium ABCD, AB || CD and AB = 2CD. Its diagonals intersect at O. If the area of ΔAOB = 84 cm², then the area of ΔCOD is equal to

• 72 cm²

• 21 cm²

• 42 cm²

• 42 cm²

Quadrilateral ABCD is circumscribed about a circle. If the lengths of AB, BC and CD are 7 cm, 8.5 cm and 9.2 cm respectively, then the length ( in cm) of DA is

• 7.7

• 16.2

• 10.7

• 10.7

The area of an isosceles trapezium is 176 cm² and the height is  of the sum of its parallel sides. If the ratio of the length of the parallel sides is 4 : 7, then the length of a diagonal (in cm) is

• 28

• √137

• 2√137

• 4√137

ABCD is a cyclic trapezium in which AD || BC. If ∠ABC = 70°, then ∠BCD is

• 110°

• 80°

• 70°

• 90°

Let Δ ABC and Δ ABD be on the same base AB and between the same parallels AB and CD. Then the relation between areas of Δ ABC and Δ ABD will be

• Δ ABD = 1/3 Δ ABC

• Δ ABD = 1/2 Δ ABC

• Δ ABC = 1/2 Δ ABD

• Δ ABC = 1/3 Δ ABD

PQRSTU is a cyclic hexagon. Then ∠P + ∠R + ∠T is equal to:

• 720°

• 360°

• 540°

• 180°

ABCD is a trapezium in which AD || BC and AB = DC = 10 m. Then the distance of AD from BC is

• 10√2 m

• 4√2 m

• 5√2 m

• 6√2 m

In a cyclic quadrilateral ABCD, the side AB is extended to a point X. If ∠XBC = 82° and ∠ADB = 47°, then the value of ∠BDC is

• 40°

• 35°

• 30°

• 25°

Three angles of a quadrilateral are 60°, 90° and 100°. Then the fourth angle of the quadrilateral is:

• 95°

• 100°

• 110°

• 115°

30.

The diagonals of AC and BD of a cyclic quadrilateral ABCD intersect each other at the point P. Then, it is always true that

• AP . CP = BP. DP

• AP. BP = CP. DP

• AP. CD = AB. CP

• BP. AB = CD. CP