For the following questions answer them individually
If $$a + \frac{1}{b} = b + \frac{1}{c} = c + \frac{1}{a}$$(where a ≠b ≠c), then abc is equal to
If $$ax + by = 1 and bx + ay = \frac{2ab}{a^2 + b^2} then (x^2 + y^2)(a^2 + b^2)$$ is equal to
ABCD is a cyclic quadrilateral of which AB is the diameter. Diagonals AC and BD intersect at E. If $$\angle DBC = 35^\circ$$, Then $$\angle AED$$ measures
In a triangle ABC, $$\angle A = 70^\circ, \angle B = 80^\circ$$ and D is the incentre of $$\triangle ABC$$. $$\angle ACB = 2x^\circ$$ and $$\angle BDC = y^\circ$$. The values of x and y, respectively are
In a right angled triangle $$\triangle$$DEF, if the length of the hypotenuse EF is 12 cm, then the length of the median DX 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
PQRA is a rectangle, AP = 22 cm, PQ = 8 cm. $$\triangle$$ABC 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
