AB is the chord of a circle with centreO. AB is produced to C, such that BC =OB, CO is joined and produced to meet the circle in D.
If `angle ACD=Y^@` and `angle AOD=x^@`, Prove that `x = 3y`.

In the figure given below, AB is the chord of a circle with centre O. AB is extended to C such that BC = OB. The straight line Co is produced to meet the circle at D. If ACD = y and AOD = x, such that x = ky, then the value of k is.

AB is a chord in a circle with centre O. AB is produced to C such that BC is equal to the radius of the circle. C is joined to O and produced to meet the circle at D. If angle ACD = 32^@ , then the measure of angle AOD is .......

In the figure AB is the chord of a circle with centre O and DOC is a line segment such that BC=DO . If /_C=20^(@) , find angle AOD.

In a triangle ABC, if AB=AC and AB is produced to D such that BD=BC, find /_ACD:/_ADC

AOB is a diamter of a circle with centreO, C is any point on the circle If AC = 6cm and BC = 8cm then AB=

AB and CD are equal chords of a circle whose centre is O,when produced these chords meet at E,Prove that EB=ED

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.

Two chords AB and CD of the circle with centre at O intersect each other at an internal point P of the centre. Prove that angle AOD+ angle BOC=2 angle BPC

In a circle with centre O, AOC is a diameter of the circle, BD is a chord and OB and CD are joined. If angle AOB = 130^@ , then angle BDC is equal to