In the figure, AB is diameter of a circle with centre O and QC is a tangent to the circle at C.If \(\angle CAB=30^0,\ find \ \angle CQA\ and \angle CBA.\) 

4

(a)

In figure, PA are two tangents drawn from an external point P to a circle with centre O.Prove that OP is the right bisector of line segment AB.

4

(a)

AB is a chord of length 24cm of a circle of radius 13cm.The tangents at A and B intersect at a point C.Find the length AC.

4

(a)

Two circles with centres O and O' of radii 3cm and 4cm, respectively intersect at two points P and Q such that OP and O'P are tangents to the two circles.Find the length of the common chord PQ.

4

(a)

In figure, the common tangent, AB and CD are tangents to two circles with centres O and O' intersect at E. Prove that the points O, E, O' are collinear.

4

(a)

Two circles touch each other externally at C.AB and CD are two common tangents.If D lies on AB such that CD=6cm, then find AB.

4

(a)

The radius of the incircle of a triangle is 6 cm and the segments into which one side is divided by the point of contact are 9 cm and 12 cm. Determine the other two sides of the triangle.

4

(a)

In the given figure, O is the centre of the circle. Determine ㄥAOC, if DA and DCare tangents and ㄥADC = 50⁰.

4

(a)

Prove that the lengths of the tangents drawn from an external point to a circle are equal.

4

(a)