Question

If 8 points in a plane are chosen to lie on or inside a circle of diameter 2cm then show that the distance between some two points will be less than 1cm. how should i proceed for this?

Answer 1

For a circle of diameter 2cm, the circumference = 2pi cm = 6.283cm. For the points to be spaced at least 1cm away, we can place 7 points (one each at 1 cm marks along the circumference of the circle, and one point at the origin - take note that the distance between the 6th point and the 1st point is 0.283cm<1cm). The 8th point will have to be placed elsewhere in (or on the circumference of) the circle, implying that the distance between this 8th point and at least one of the other points will be less than 1cm.