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If 7 points are chosen inside or on the unit circle, then How many points are there which are at a distance at most 1 unit?

If 7 points are chosen inside or on the unit circle, then How many points are there which are at a distance at most 1 unit? Correct Answer Atleast 2

Concept:

Pigeon-hole principle

1. If n pigeonholes are occupied by n + 1 or more pigeons, then at least one pigeonhole is occupied by greater than one pigeon.

2. Generalized pigeonhole principle is: - If n pigeonholes are occupied by kn + 1 or more pigeons, where k is a positive integer, then at least one pigeonhole is occupied by k + 1 or more pigeons.

Analysis:

Divide the circle into 6 equal sectors by drawing radii so that angle between two consecutive radii is π/3.

By the Pigeon-hole principle, there is a sector containing at least two points.

The distance between these two points is at most 1

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