In the adjoining figure, O is the centre and seg AB is a diameter. At point C on the circle, the tangent CD is drawn. Line BD is tangent at B . Prove that seg OD `||` seg AC.

In the adjoining figure, chord AB ~= chord CD . Prove that arc AC ~= BD

In figure if PR is tangent to the circle at P and O is the centre of the circle then angle POQ is

In the adoining figure, A is the centre of the circle. Poin D is in the exterior of the circle. Line DP and Line DQ are tangents at points at P and Q respectively. Prove that DP=DQ.

In the adjoining figure, seg AB is a diameter of a circle with centre C . Line PQ is a tangent, it touhces the circle at T. segs AP and BQ are perpendiculars to line PQ. Prove seg CP ~= seg CQ .

In the adjoining figure the circles with centers P and Q touch each other at R . A line passing through R meets the circles at A and B respectively then Prove that : (i) seg AP|| seg BQ. (ii) DeltaAPR~DeltaRQB . (iii) Find angleRQB if anglePAR = 35^(@)

In figure if PR is tangent to the circle at P and O is the centre of the circle, then anglePOQ is ____.

In the adjoining figure seg RS is the dianeter of the circle with centre 'O' . Point T is in the exterior of the circle . Prove that angleRTS is an acute angle.

In the adjoining figure, seg EF is the diameter of the circle with centre H . Line DF is tangent at point F . If r is the radius of the circle, then prove that DExxGE=4r^(2) To Prove : DExxGE=4r^(2)

In the adjoining figure point O is the centre of the circle . Line PB is a tangent and line PAC is a secnt. Find Paxx PC if OP = 25 and radius is 7 .