In a circle with centre 'O' . `bar(AB)` is a chord and 'M' is its midpoint . Now prove that `angle (OM)` is perpendicular to AB

In a circle with centre 'O'. bar(AB) is chord and 'M' is its midpoint. Now prove that bar(OM) is perpendicular to AB. (Hint : Join OA and OB consider triangles OAM and OBM)

In the adjacent figure, AB is a chord of circle with centre O. CD is the diameter perpendicualr to AB. Show that AD = BD.

In the figure, O is the centre of the circle and AB = CD. OM is perpendicular on bar(AB) and bar(ON) is perpendicular on bar(CD) . Then prove that OM = ON.

If two circles intersect at two points , then prove that their centres lie on the perpendicular bisector of the common chord.

Two tangents TP and TQ are drawn to a circle with centre 'O' from on external point T. Prove that angle PTQ = 2 angle OPQ .

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 = 60^@ .

If A(10,4),B(-4,9) and C(-2,-1) are the vertices of a triangle. Find the equation (i) bar(AB) (ii) the media through A (iii) the altitude through B (iv) the perpendicular bisector of the side bar(AB) .

In the figure XY and X'Y' are two parallel tangents to a circle with centre O and another tangent AB with point of cantact C intersecting XY at A and X'Y' at B then angle AOB=