In figure, `bar(AB)` is a diameter of the circle, `bar(CD)` is a chord equal to the radius of the circle. `bar(AC)` and `bar(BD)` when extended intersect at a point E. Prove that `angle AEB = 6^@`.

In the abjoining figure, point O is the centre of the circle . Length of chord AB is equal to the radius of the circle . Find (i) angleAOB (ii) angleACB (iii) nm (arc AB) (iv) m (arc ACB)

AB is a diameter of a circle. CD is a chord parallel to AB and 2CD = AB . The tangent at B meets the line AC produced at E then AE is equal to -

Find the radius and centre of the circle z bar(z) - (2 + 3i)z - (2 - 3i)bar(z) + 9 = 0 where z is a complex number

In the given figure, AB is the diameter of the circle, centered at O. If angleCOA = 60^(@), AB = 2r, AC = d, and CD = l , then l is equal to

If one of the diameters of the circle x^2+y^2-2 x-6 y+6 =0 is a chord to the circle with centre at (2,1) then the radius of the circle is equal to.

In the adjoining figure, two circles intersect each other at points A and E . Their common secant through E intersects the circle at points B and D . The tangents of the circles at point B and D intersect each other at point C . Prove that squareABCD is cyclic .

In the adjoining figure,seg AB is a diameter of a circle with centre O . Bisector of inscribed angleACB intersects circle at point D. Complete the following proof by filling in the blanks. Prove that : seg AD ~= seg BD

In the given figure A,B,C and D are four points on a circle, AC and BD intersect at a point E such that angleBEC=130^(@) and angleECD=20^(@) . Find angleBAC .