`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.

Find the area of an equilateral triangle inscribed in the circle x^2 + y^2 + 2gx + 2fy + c = 0

P and Q are two points ona circle with centre at O. R is a point on the minor arc of the circle, between the points P and Q. The tangents to the circle at the points P and Q meet each other at the points S. If anglePSQ =20^@ , then anglePRQ =

Find the area of the equilateral triangle inscribed in the circle x^(2) + y^(2) + 2gx + 2fy + c = 0 .

P is any point inside the circle with centre O. Calculate the minimum length of chord through P if the radius of the circle is 5cm and OP= 3cm.

P is a point within a circle with centre O. If the radius of the circle is 13cm. And OP = 12cm, then the length of the least chord through P is

P is the variable point on the circle with center at C. C A and C B are perpendiculars from C on the x- and the y-axis, respectively. Show that the locus of the centroid of triangle P A B is a circle with center at the centroid of triangle C A B and radius equal to the one-third of the radius of the given circle.

P(a,5a) and Q(4a,a) are two points. Two circles are drawn through these points touching the axis of y. Centre of these circles are at

A point P is given on the circumference of a circle of radius r. The chord QR is parallel to the tangent line at P. Find the maximum area of the triangle PQR.

If a point P is 17 cm from the centre of a circle of radius 8 cm, then find the length of the tangent drawn to the circle from point P.