A circle centred at 'O' has radius 1 and contains the point A. Segment AB is tangent to the circle at A and `angleAOB =theta`. If point C lies on OA and BC bisects the angle ABO then OC equals

In figure PQ is tangent to the circle with centre at O at the point B , if angle AOB = 100^(@) , then angle ABP is equal to

In figure-3, PQ is tangent to the circle with centre at O, at the point B. if angleAOB=100^(@) , then angleABP is equal to

The congruent circles with centres Oand O' intersect at two points A and B. Then, angleAOB=angleAO'B .

A circle has its centre at the origin and a point P (5,0) lies on it . The point Q (6,8) lies outside the circle.

The figure shows two circles with the same center O. Line segment bar(AB) ios tangent to the smaller circle . If OA=5 and AB=12.what is the ratio of the area of the smaller circle to the area of the larger circle ?

AB is the diameter of a circle with centre O. A line PQ touches the given circle at point R and cuts the tangents to the circle through A and B at points P and Q respectively. Prove that /_POQ=90^(@)

A is a point at a distance 13 cm from the centre O of a circle of radius 5 cm. AP and AQ are the tangents to the circle at P and Q. If a tangent BC is drawn at a point R lying on the minor arc PQ to intersect AP at B and AQ at C, find the perimeter of the Delta ABC

The circle above with centre A has an area of 21. BC is tangent to the circle with centre A at point B. IF AC=2AB, then what is the area of the shaded region?

The line 2x - y + 1 = 0 is tangent to the circle at the point (2,5) and the centre of the circles lies on x-2y = 4. The radius of the circle is :

A circle of radius 2 has its centre at (2, 0) and another circle of radius 1 has its centre at (5, 0). A line is tangent to the two circles at point in the first quadrant. The y-intercept of the tangent line is