`Pa n dQ` are two points on a circle of centre `C` and radius `alpha` . The angle `P C Q` being `2theta` , find the value of `sintheta` when the radius of the circle inscribed in the triangle `C P Q` is maximum.

In a right angled triangle A B C , right angled at B ,\ B C=12 c m and A B=5c m . The radius of the circle inscribed in the triangle (in cm) is :

An isosceles triangle of vertical angle 2theta is inscribed in a circle of radius a . Show that the area of the triangle is maximum when theta=pi/6 .

If the tangent at a point P to a circle with centre O cuts a line through O at Q such that P Q=24 c m and O Q=25 c m . Find the radius of the circle.

P Q is a chord of length 8 cm of a circle of radius 5 cm. The tangents at P and Q intersect at a point T . Find the length T P .

A point P is 13cm from the centre of the circle. The length of the tangent drawn from P to the circle is 12 cm. Find the radius of the circle.

Make a point P and draw a circle with centre P and radius 5 cm. Take any point Q on the circle drawn. With Q as centre and radius 3 cm draw another circle. Label the two points at which the circles intersect as A and B. Join PQ and AB. Find the angle between AB and PQ.

A circle is inscribed in an equilateral triangle A B C of side 12 cm, touching its sides (Figure). Find the radius of the inscribed circle and the area of the shaded part.

ABC is a right angled triangle with AB=12 cm and AC=13 cm. A circle, with centre O has been inscribed inside the triangle. Calculate the value of x, the radius of the inscribed circle.

The centres of the circles are (a, c) and (b, c) and their radical axis is y-axis. The radius of one of the circles is r. The radius of the other circle is

Draw a circle of radius 3 cm. Take a point P outside it. Without using the centre of the circle, draw two tangents to the circle from the point P.