MathDB

3

Part of 1985 Greece National Olympiad

Problems(2)

lake visibilty problem - 1985 Greece MO X p3

Source:

9/8/2024
Interior in alake there are two points A,BA,B from which we can see every other point of the lake. Prove that also from any other point of the segment ABAB, we can see all points of the lake.
geometryangles
min distance of lattice point from 5x-10y+3=0 is \sqrt3/ 20

Source: 1985 Greece MO Grade XII p3

9/6/2024
Consider the line (E): 5x−10y+3=05x-10y+3=0 . Prove that: a) Line (E)(E) doesn't pass through points with integer coordinates. b) There is no point A(a1,a2)A(a_1,a_2) with a1,a2∈Z a_1,a_2 \in \mathbb{Z} with distance from (E)(E) less then 320\frac{\sqrt3}{20}.
analytic geometrygeometrydistancenumber theorylattice points