MathDB

3

Part of 2015 Oral Moscow Geometry Olympiad

Problems(2)

triangle reconstruction, 3 points given, 3 equal segments related

Source: Oral Moscow Geometry Olympiad 2015 grades 8-9 p3

8/8/2019
In triangle ABCABC, points D,ED, E, and FF are marked on sides AC,BCAC, BC, and ABAB respectively, so that AD=ABAD = AB, EC=DCEC = DC, BF=BEBF = BE. After that, they erased everything except points E,FE, F and DD. Reconstruct the triangle ABCABC (no study required).
geometryconstructionequal segments
S_{AOK} = S_{AOB} + S_{DOK}, areas, starting with a trapezoid

Source: Oral Moscow Geometry Olympiad 2015 grades 10-11 p3

8/6/2019
OO is the intersection point of the diagonals of the trapezoid ABCDABCD. A line passing through CC and a point symmetric to BB with respect to OO, intersects the base ADAD at the point KK. Prove that SAOK=SAOB+SDOKS_{AOK} = S_{AOB} + S_{DOK}.
areastrapezoidgeometry