Question

For a circle with centre O and radius 5 cm, which of the following statements is true ? P : Distance between every pair of parallel tangents is 5 cm. Q : Distance between every pair of parallel tangents is 10 cm. R : Distance between every pair of parallel tangents must be between 5 cm and 10 cm. S : There does not exist a point outside the circle from where length of tangent is 5 cm.

There is a circular park of diameter 65 m as shown in the following figure, where AB is a diameter. An entry gate is to be constructed at a point P on the boundary of the park such that distance of P from A is 35 m more than the distance of P from B. Find distance of point P from A and B respectively.