Problems(2)
one side of triangle is twice as another, AI=MI, incenter related
Source: Czech-Polish-Slovak Junior Match 2015, Team p1 CPSJ
3/19/2020
Let be the center of the circle of the inscribed triangle and be the center of its side .
If , prove that there are two of the sides of triangle , of which one is twice of the other.
geometryincenter
find angle such that a triangle has the largest area, inside a right triangle
Source: Czech-Polish-Slovak Junior Match 2015, Individual p1 CPSJ
3/14/2020
In the right triangle with shorter side the hypotenuse has length . Denote its centroid and the feet of altitude from the vertex . Determine the size of its inner angle at the vertex for which the triangle has the greatest possible area.
geometrymaxarea of a triangleangleright triangle