Question

A rectangular floor area can be completely tiled with 200 square tiles. If the side length of each tile is increased by 1 unit, it would take only 128 tiles to cover the floor.

A backyard is in the shape of a triangle ABC with right angle at B. AB = 7 m and BC = 15 m. A circular pit was dug inside it such that it touches the walls AC, BC and AB at P, Q and R respectively such that AP = x m.

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.