MathDB

3

Part of 2021 Argentina National Olympiad

Problems(3)

Argentina MO 2021 National Level 1 P3

Source:

4/23/2022
Let ABCABC be an isosceles right triangle at AA with AB=ACAB=AC. Let MM and NN be on side BCBC, with MM between BB and N,N, such that BM2+NC2=MN2.BM^2+ NC^2= MN^2. Determine the measure of the angle ∠MAN.\angle MAN.
geometryright triangleAngle Chasingcontests
Argentina MO 2021 National Level 2 P3

Source:

4/23/2022
A circle is divided into 2n2n equal arcs by 2n2n points. Find all n>1n>1 such that these points can be joined in pairs using nn segments, all of different lengths and such that each point is the endpoint of exactly one segment.
geometryarcslengthscontests
Argentina MO 2021 National Level 3 P3

Source:

4/24/2022
Let ABCDABCD be a quadrilateral inscribed in a circle such that ∠ABC=60∘.\angle ABC=60^{\circ}.
a) Prove that if BC=CDBC=CD then AB=CD+DA.AB= CD+DA. b) Is it true that if AB=CD+DAAB= CD+DA then BC=CDBC=CD?
geometryAngle ChasingArgentina