If C1, C2 be the centres of two circles and r1, r2 be the respective radii such that the distance between the centres is equal to the sum of the radii of the two circle, find the number of common tangents.

Two circles touch each other externally at P. AB is a direct common tangent touching them respectively at A and B, then ∠APB is:

​Number of circles through a pair of given points​

In the diagram , AD is the tangent line of the circle and ABC is the secant line. If AB = 4 cm and BC = 5 cm, then the length of AD is

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Five concentric, adjacent, semi-circular running tracks, each of mean length 100 m and width 2.5 m are marked on a field. If the angle subtended by inner track is 1.00 rad, the angle subtended by the outermost track is

Two circles of radii 9.0 units and 4.0 units touch each other externally as in the figure. Then the length (in units) of their common tangent AB is

PN is a secant intersecting a circle at points M and N such that PN > PM. A tangent PT is drawn to the circle touching it at T. If PM = 32 cm and PT = 40 cm, what is the length (in cm) of the chord MN?

​Two intersecting circles are said to be orthogonal if the angle between them is a/an _________.​​

ABC is a right angled triangle. A circle is inscribed in it. The length of the two sides containing the right angle are 10 cm and 24 cm. find the radius of the circle.

A circle having centre c1, radius r1 = 5 cm is placed against a right angle. another smaller circle having centre c2, radius r2 is also placed touching the sides of angle and the bigger circle as shown in the figure. Find the radius r2, in cm, of the smaller circle.