In the figure, O is the center of the circle and BO is the bisector of angle ABC show that AB=BC

In the following figure, O is the centre of the circle. AB is an arc of the circle, such that angle AOB=80^@ .Find angle ACB .

In Figure,AB=CB and O is the centre of the circle.Prove that BO bisects /_ABC .

In the given figure, O is the centre of a circle and arc ABC subtends an angle of 130^(@) at O. AB is extended to P, Then, anglePBC is equal to

In the given figure, AB is the diameter of the circle, centered at O. If angle COA =60^(@), AB=2r, Ac=d and CD=l, then l is equal to

In the figure,BC is a chord of the circle with centre o and A is a point on the minor are BC. Then /_ABC-/_OBC is equal to

Two variable chords AB and BC of a circle x^(2)+y^(2)=a^(2) are such that AB=BC=a . M and N are the midpoints of AB and BC, respectively, such that the line joining MN intersects the circles at P and Q, where P is closer to AB and O is the center of the circle. The locus of the points of intersection of tangents at A and C is

If two chords AB and AB of a circle with centre O are such that the centre O lies on the bisector of /_BAC; Prove that AB=AC