MathDB

7

Part of 2023 Novosibirsk Oral Olympiad in Geometry

Problems(3)

collinearities by 2 squares (2023 Novosibirsk Oral Geo Oly 7.7)

Source:

9/4/2023
Squares ABCDABCD and BEFGBEFG are located as shown in the figure. It turned out that points A,GA, G and EE lie on the same straight line. Prove that then the points D,FD, F and EE also lie on the same line. https://cdn.artofproblemsolving.com/attachments/4/2/9faf29a399d3a622c84f5d4a3cfcf5e99539c0.png
geometrycollegeSquares
2 // lines intersect a square (2023 Novosibirsk Oral Geo Oly 8.7)

Source:

9/4/2023
A square with side 11 is intersected by two parallel lines as shown in the figure. Find the sum of the perimeters of the shaded triangles if the distance between the lines is also 11. https://cdn.artofproblemsolving.com/attachments/9/e/4e70610b80871325a72e923a0909eff06aebfa.png
geometrysquareParallel Lines
<EDC = 2< BCD = 2< CAB, 100-60-20 (2023 Novosibirsk Oral Geo Oly 9.7)

Source:

9/5/2023
Triangle ABCABC is given with angles ∠ABC=60o\angle ABC = 60^o and ∠BCA=100o\angle BCA = 100^o. On the sides AB and AC, the points DD and EE are chosen, respectively, in such a way that ∠EDC=2∠BCD=2∠CAB\angle EDC = 2\angle BCD = 2\angle CAB. Find the angle ∠BED\angle BED.
anglesgeometry