MathDB

2

Part of 2015 Oral Moscow Geometry Olympiad

Problems(2)

angle wanted, square and equilateral related

Source: Oral Moscow Geometry Olympiad 2015 grades 8-9 p2

8/8/2019
The square ABCDABCD and the equilateral triangle MKLMKL are located as shown in the figure. Find the angle ∠PQD\angle PQD. https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjQKgjvzy1WhwkMJbcV_C0iveelYmm75FpaGlWgZ-Ap_uQUiegaKYafelo-J_3rMgKMgpMp5soYc1LVYLI8H4riC6R-f8eq2DiWTGGII08xQkwu7t2KVD4pKX4_IN-gC7DVRhdVZSjbaj2S/s1600/oral+moscow+geometry+2015+8.9+p2.png
geometryangleEquilateralsquare
midpoint wanted, 3 perpendicular bisectors related

Source: Oral Moscow Geometry Olympiad 2015 grades 10-11 p2

8/6/2019
Line ℓ\ell is perpendicular to one of the medians of the triangle. The perpendicular bisectors of the sides of this triangle intersect line ℓ\ell at three points. Prove that one of them is the midpoint of the segment formed by the remaining two.
geometryperpendicular bisectormidpoint