`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.

P and Q are two points on a circle of centre C and radius alpha. The angle PCQ being 2 theta ,find the value of sin theta when the radius of the circle inscribed in the triangle CPQ is maximum.

If P (x,y) and Q (1,4) are the points on the circle whose centre is :C(5,7) and radius is 5 cm, then find the locus of P.

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.

Find the centre and radius of the circle passing through the points P (-7,4) ,Q(0,3) and R (-4,5)

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.

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

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.

A tangent is drawn from an external point O to a circle of radius 3 units at P such that OP = 4 units. If C is the centre of the circle, then the sine of the angle COP is