`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.

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

The two tangents from an external points P to a circle with centre at O are PA and PB. If angle APB=70^(@) then the value of angle AOB is

The two tangents from an external points P to a circle with centre at O are PA and PB. If angle APB=70^(@) then the value of angle AOB is

In the adjoining figure, point P is the centre of the circle and line AB is the tangent to the circle at T . The radius of the circle is 6 cm . Find PB if angleTPB=60^(@)

P is the variable point on the circle with center at CdotC 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.

Draw a circle with centre O and radius 3.5 cm. Draw tangents PA and PB to the circle, from a point p outside the circle, at points A and B respectively. angleAPB=80^(@).

C is the centre of the circle with centre (0,1) and radius unity. y=ax^2 is a parabola. The set of the values of 'a' for which they meet at a point other than the origin, is

Draw a circle with O as centre and radius 3.8 cm. Take two points P and Q such that anglePOQ=120^(@) Draw tangents at P and Q without using centre.