MathDB

1

Part of 2019 Taiwan TST Round 3

Problems(2)

Sum of Numbers in Rectangle isnt Prime

Source: 2019 Taiwan TST Round 3

4/2/2020
For each lattice point on the Cartesian Coordinate Plane, one puts a positive integer at the lattice such that for any given rectangle with sides parallel to coordinate axes, the sum of the number inside the rectangle is not a prime. Find the minimal possible value of the maximum of all numbers.
analytic geometrygeometryrectangle
Perpendicularity in the configuration consisting of Four Circumcenters

Source: 2019 Taiwan TST Round 3, Test 1, Problem 1

4/26/2019
Given a △ABC \triangle ABC and a point P. P. Let O O, DD, EE, FF be the circumcenter of △ABC \triangle ABC, △BPC\triangle BPC, △CPA\triangle CPA, △APB,\triangle APB, respectively and let T T be the intersection of BC BC with EF. EF. Prove that the reflection of O O in EF EF lies on the perpendicular from D D to PT. PT.
Proposed by Telv Cohl
geometrygeometry proposed