9.9
Problems(2)
square , 4 right isosceles triangles -VI Soros Olympiad 1999-00 Round 1 9.9
Source:
5/21/2024
On the plane there are two isosceles non-intersecting right triangles and ( and are the hypotenuses, is a convex quadrilateral), and . Let's construct two more isosceles right triangles: (with hypotenuse located outside triangle ) and (with hypotenuse located outside triangle ). Prove that the line passes through a point such that is a square.
geometrysquare
min area of a triangle inscribed in a right angle
Source: VI Soros Olympiad 1990-00 R1 9.9 https://artofproblemsolving.com/community/c2416727_soros_olympiad_in_mathematics
5/27/2024
The center of a circle, the radius of which is , lies on the bisector of the right angle at a distance from its sides (). A tangent to the circle intersects the sides of the angle at points and . Find the smallest possible value of the area of triangle .
geometrygeometric inequalityright angle