MathDB

1

Part of 2012 Oral Moscow Geometry Olympiad

Problems(2)

trapezoid AD//BC, AB = BC = BD, altitude BK cuts AC at M, <CDM?

Source: 2012 Oral Moscow Geometry Olympiad grades 8-9 p1

9/8/2019
In trapezoid ABCDABCD, the sides ADAD and BCBC are parallel, and AB=BC=BDAB = BC = BD. The height BKBK intersects the diagonal ACAC at MM. Find ∠CDM\angle CDM.
geometrytrapezoidanglesequal segments
incenter inside the midpoint's line triangle?

Source: 2012 Oral Moscow Geometry Olympiad grades 10-11 p1

9/25/2019
Is it true that the center of the inscribed circle of the triangle lies inside the triangle formed by the lines of connecting it's midpoints?
geometryincentermidpoints