MathDB

3

Part of 2017 Oral Moscow Geometry Olympiad

Problems(2)

is it true that ABCD is parallelogram ?

Source: 2017 Oral Moscow Geometry Olympiad grades 8-9 p3

7/26/2019
Points MM and NN are the midpoints of sides ABAB and CDCD, respectively of quadrilateral ABCDABCD. It is known that BC//ADBC // AD and AN=CMAN = CM. Is it true that ABCDABCD is parallelogram?
geometryparallelogrammidpoints
unmarked ruler diameter of circumcircle at 7 steps construction

Source: 2017 Oral Moscow Geometry Olympiad grades 10-11 p3

7/25/2019
On the plane, a non-isosceles triangle is given, a circle circumscribed around it and the center of its inscribed circle are marked. Using only a ruler without tick marks and drawing no more than seven lines, construct the diameter of the circumcircle.
geometrycircumcircleconstructionRuler