MathDB

2#

Part of 2020 Candian MO

Problems(1)

1st Problem [< MAB = 10°, ... ==> triangle ABC isosceles]

Source: USAMO 1996, Problem 5

2/3/2003
Let ABCABC be a triangle, and MM an interior point such that ∠MAB=10∘\angle MAB=10^\circ, ∠MBA=20∘\angle MBA=20^\circ, ∠MAC=40∘\angle MAC=40^\circ and ∠MCA=30∘\angle MCA=30^\circ. Prove that the triangle is isosceles.
USAMOtrigonometryiscosceles triangleLaw of CosinesLaw of Sinesreflectiongeometry