A straight line intersects thethree concentric circles at A, B, C. if the distance of line from the centre of the circles is 'P', prove that the area of the triangle formed by tangents to the circle at A, B, C is `((1)/(2P).AB.BC.CA)`.

Draw a circle of radius 3 cm. Take a point P at a distance of 5 cm from the centre of the circle. From P, construct a pair of tangents to the circle.

If a line intersects two concentric circles (circles with the same centre) with centre O at A, B, C and D, prove that AB = CD (see Fig. 10.25).

Point O is the centre of a circle . Line a and line b are parallel tangents to the circle at P and Q. Prove that segment PQ is a diameter of the circle.

There are two concentric circles such that the area of the outer circle is four times the area of the inner circle. Let A, B and C be three distinct point on the perimeter of the outer circle such that AB and AC are tangents to the inner circle. If the area of the outer circle is 12 square centimeters then the area (in square centimeters) of the triangle ABC would be:

In the figure, O is the centre of the circle . Seg AB is the diameter at the point C on the circle the tangent CD is drawn. Line BD is a tangent to the circle at point B. Show that seg OD || chord AC.

A straight line is drawn through the centre of the circle x^(2)+y^(2)-2ax=0 line x+2y=0 parallel to the straight and intersecting the circle at A and B. Then the area of triangle AOB is

In Figure,l is a line intersecting the two concentric circles,whose common centre is O, at the points A,B,C and D. Show that AB=CD

In Figure,l is a line intersecting the two concentric circles,whose common centre is O, at the points A,B,C and D. Show that AB=CD