AB is a diameter of a circle. CD is a chord parallel to AB and `2CD = AB`. The tangent at B meets the line AC produced at E then AE is equal to -

AB is a diameter of a circle with centre at O. If chord CD bot AB and angleCAD = 80^@ , then angleADC =

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^@ .

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 and CD are two diameters of a circle. Prove that ADBC is a rectangle

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 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. 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 at O. Chord PQ intersects AB in such a way that angleAOP = 130^@ . The value of anglePQB is

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.

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 .