`PQ` is a diameter of a circle and `AB` is such a chord of it that it is perpendicular to `PQ`. If `C` be the point of intersection of `PQ` and `AB`, then prove that `PC.QC=AC.BC`.

AB is a diameter of a circle. PQ is such a chord of the circle that it is neither a diameter of the circle nor a interceptor of AB. By joining the points A, P and B, Q it is found that ABQP is a quadrilateral of wich angleBAP=angleABQ . Prove that ABQP is a cyclic trapezium.

AB is a diameter of a circle and AC is its chord such that angleBAC=30^(@) . If the tengent at C intersects AB extended at D, then BC=BD.

AB is a diameter of a circle and AC is its chord such that angleBAC=30^(@) . If the tengent at C intersects AB extended at D, then BC=BD.

AB is a diameter of a circle and AC is its chord such that angleBAC=30^(@) . If the tengent at C intersects AB extended at D, then BC=BD.

In the given figure, PQ||AB and PR||AC . Prove that QR||BC

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.

AB is a diameter and AC is a chord of a circle with centre O such that angleBAC=30^@ . The tangent at C intersects AB at a point D. Prove that BC=BD.

In the adjoining figure, chord Pq and chord AB intersect at pointM . If PM = AM, then prove that BM = QM.

In the adjoining figure,chord PQ and chord AB intersect at point M.If PM=AM,then prove that BM=QM.