`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`.

QR is a chord of the circle with centre at O and POR is a diamter of it. OD is perpendicular to QR. If OD= 4 cm , then the length of PQ is

If A,B,C are three points on a line and B lies between A and C, then prove that AC-AB = 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 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.

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 .

Two chords AB and CD of a circle are perpendicular to each other. If perpendicular drawn to AD from the point of intesection of those two chords AB and CD is produced to meet BC at the point E prove that the point E is the mid- point of 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.

Three points P,Q ,R lie on a circle. The two perpendiculars PQ and PR and the point P intersect the circle at the points S and T respectively. Prove that RQ=ST

PQ is a diameter of the circle with centre at O. The tengent drawn at A on the circle intersect the extended PQ at R. If angle PRA=45^(@), then angle OAP=