4
Problems(2)
triangle construction, given 1 side, inradii, respective exradii
Source: 2009 Oral Moscow Geometry Olympiad grades 8-9 p4
9/19/2020
Construct a triangle given a side, the radius of the inscribed circle, and the radius of the exscribed circle tangent to that side. (Research is not required.)
geometryconstruction
concurrent wanted, circles with medians as diamaters intersect in pairs
Source: 2009 Oral Moscow Geometry Olympiad grades 10-11 p4
9/14/2020
Three circles are constructed on the medians of a triangle as on diameters. It is known that they intersect in pairs. Let be the intersection point of the circles built on the medians and , which is more distant from the vertex . Points and are defined similarly. Prove that the lines and intersect at one point.(D. Tereshin)
geometryconcurrencyconcurrentMediansdiameter