Let A, B be the centres of two circles of equal radii, draw them so that each one of them passes throught the centre of the other. Let them intersect at C and D. Examine whether AB and CD are at right angles.

"If two circles each other externally them the point of contact and the centres are collinear" Prove this.

To draw a pair of tangents to a circle inclined to each other at 40^@ , the angle at the centre of the circle between the two radii is _______

In the figure ,A and B are the centres of two circles with radii 6 cm and 2 cm respectively .CD is the diameter then MD is equal to :

To draw a pair of tangents to a circle inclined to each other at an angle of 60^@ , it is required to draw the two radii of the circle intersecting at an angle of

The diameter of a circle is a line which joins two points on the circle and also passes through the centre of the circle. (In the adjoining figure (Fig 11.12) AB is a diameter of the circle, C is its centre.) Express the diameter of the circle (d) in terms of its radius (r).

Let AB be a chord of the circle x^2+y^2=a^2 subtending a right angle at the centre. Then the locus of the centroid of triangle PAB as P moves on the circle is:

Two circles intersect each other. Then the total number of common tangents that can be drawn to them is :

Two chords AB and CD of length 5 cm and 11 cm respectively of a circle are parallel to each other and are on opposite sides of its centre. If the distance between AB and CD is 6 cm, find the radius of the circle.

Two poles of equal height are standing opposite to each other on the either side of the road which is 80 m wide. From a point P between them on road, the angle of elevation of the top of a pole is 60^(@) and the angle of depression from the top of another pole at point P is 30^(@) . Find the heights of the poles and distances of the point P from the poles.