`AB` is a diameter of a circle. `BP` is a tangent to the circle at `B`. A straight line passing through `A` intersects `BP` at `C` and the circle at `D`. Prove that `BC^(2)=ACxxCD`.

AB is a diameter of a circle. C is any point on the circle, angleACB=

Two circles intersect each other at the points P and Q. A straight line passing through P intersects one circle at A the other circle at .A straight line passing through Q intersect the first circle at C and the second circle at D. Prove that AC||BD .

AB is a diameter of a circle and 'C' is any point on the circumference of the circle .Then

Two circle intersect each other at A and B and a straight line parallel to AB intersects the circles at C,D,E,F. Prove that CD = EF.

AB is a diameter of a circle with centre O . A line drawn through the point A intersects the circle at the point C and the tangent through B at the point D . Prove that (a) BD^(2)=AD.DC . (b) The area of the rectangle of formed by AC and AD for any straight line is always equal.

Draw circle passing through A, B where AB = 5.4cm

AB is a diameter of a circle with centre O and AC is a chord . The straight line through O parallel to AC meets the arc BC at D. Prove that, BD= CD.

XY is a diameter of a circle. PAQ is a tangent to the circle at the point A lying on the circumference. The perpendicular drawn on the tangent to the circle from X intersects PAQ at Z. Prove that XA is a bisector of angle YXZ." "[GP-X]

P is a point inside a circel: NO tangent of the circle will pass through P.

AB is a diameter and AC is a chord of the circle with centre at Q. the radius parallel to AC intersect the circle at D. Prove that D is the mid-point of the are BC.