MathDB

4

Part of 2003 Portugal MO

Problems(1)

10 houses in a circle, different routes, different distances 2003 Portugal p4

Source:

10/13/2020
In a village there are only 1010 houses, arranged in a circle of a radius rr meters. Each has is the same distance from each of the two closest houses. Every year on Sunday of Pascoa, the village priest makes the Easter visit, leaving the parish house (point AA) and following the path described in Figure 1. This year the priest decided to take the path represented in the Figure 2. Prove that this year the priest will walk another 10r10r meters. https://cdn.artofproblemsolving.com/attachments/a/9/a6315f4a63f28741ca6fbc75c19a421eb1da06.png
geometryCyclicdistance