In the given figure, a circle is inscribed in such that it touches the sides PQ, QR and RP at points D, E, F, respectively. If the lengths of the sides PQ = 15 cm, QR = 11 cm and RP = 13 cm, then find the length of PD.

If the distance between center to chord is 12 cm and the length of the chord is 10 cm, then the diameter of the circle is-

In the following figure, PAB is a secant and PT is a tangent to the circle. If PT = 5 cm and PA = 3 cm, then find the measurement of AB.

If centroid of the points (3, 5), (6, y) and (-3, 4) is (x, y), then find the values of x and y.

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?