D and E are points on the sides AB and AC respectively of ΔABC such that DE is parallel to BC and AD:DB = 4:5, CD and BE intersect each other at F. Then the ratio of the areas of ΔDEF and ΔCBF

ΔABC is an isosceles right angled triangle having ∠C = 90°. If D is any point on AB, then AD2+ BD2 is equal to

PQRA is a rectangle, AP = 22 cm, PQ = 8 cm. ΔABC is a triangle whose vertices lie on the sides of PQRA such that BQ = 2 cm and QC = 16 cm .Then the length of the line joining the mid points of the sides AB and BC is

Two equal circles intersect so that their centres, and the points at which they intersect form a square of side 1 cm. The area (in sq.cm) of the portion that is common to the circles is

In a right angled triangle ΔDEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX is

In a triangle ABC, ∠A = 70°, ∠B = 80° and D is the incentre of ΔABC. ∠ACB = 2x° and ∠BDC = y°. The values of x and y, respectively are

ABCD is a cyclic quadrilateral of which AB is the diameter. Diagonals AC and BD intersect at E. If ∠DBC = 35°, Then ∠AED measures

If x, y, z are the three factors of a3 -7a - 6, then value of x+y+z will be