A triangle ABC is drawn to circumscribe a circle of radius 4 cm such that the segments BD and DC into which BC is divided by the point of contact D are of lengths 8 cm and 6 cm respectively (see Fig). Find the sides AB and AC.

2

(a)

In the given figure, AB is a diameter of the circle, with centre O and AT is a  tangent. Calculate the numerical value of x.

2

(a)

In given figure, find the perimeter of \(\angle ABC\), if AP = 10 cm.

2

(a)

Two circles intersect each other at two points A and B. From point A, tangents AP and AQ are drawn to two circles which intersect the circles at the pointsP and Q respectively. Prove that AB is the bisector of \(\angle PBQ\).

2

(a)

Let A be a point of intersection of two intersecting circles with centres O and O'. The tangents at A to the two circles meet the circles at B and C respectively. Point P is located so that AOPO; is a parallelogram. Prove that P is the circumcentre of \(\triangle ABC\).

2

(a)