Find the centre and radius of the circle .

A sector O A B O of central angle theta is constructed in a circle with centre O and of radius 6. The radius of the circle that is circumscribed about the triangle O A B , is (a) 6costheta/2 (b) 6sectheta/2 (c) 3sectheta/2 (d) 3(costheta/2+2)

In the adjoining figure, seg EF is the diameter of the circle with centre H . Line DF is tangent at point F . If r is the radius of the circle, then prove that DExxGE=4r^(2) To Prove : DExxGE=4r^(2)

A sector O A B O of central angle theta is constructed in a circle with centre O and of radius 6. The radius of the circle that is circumscribed about the triangle O A B , is 6costheta/2 (b) 6sectheta/2 c) 3sectheta/2 (d) 3(costheta/2+2)

Let ABC be an isosceles triangle with base BC. If r is the radius of the circle inscribsed in DeltaABC and r_(1) is the radius of the circle ecribed opposite to the angle A, then the product r_(1) r can be equal to (where R is the radius of the circumcircle of DeltaABC )

In the adjoining figure seg RS is the dianeter of the circle with centre 'O' . Point T is in the exterior of the circle . Prove that angleRTS is an acute angle.

A circle having centre as O' and radius r' touches the incircle of Delta ABC externally at. F, where F is on BC and also touches its circumcircle internally at G. It O is the circumcentre of Delta ABC and I is its incentre, then

Two circle with centre O and P intersect each other in point C and D. Chord AB of the circle with centre O touches the circle with circle with centre P in Point E. Prove that angleADE+angleBCE= 180^(@)

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^(@).