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Part of 2022 Novosibirsk Oral Olympiad in Geometry

Problems(2)

angles by angle bisectors given (2022 Novosibirsk Oral Geo Oly 7.3)

Source:

Three angle bisectors were drawn in a triangle, and it turned out that the angles between them are

50^o

60^o

70^o

. Find the angles of the original triangle.

geometryangle bisector

regular hexagon (2022 Novosibirsk Oral Geo Oly 9.3)

Source:

In a regular hexagon, segments with lengths from

1

6

were drawn as shown in the right figure (the segments go sequentially in increasing length, all the angles between them are right). Find the side length of this hexagon. https://cdn.artofproblemsolving.com/attachments/3/1/82e4225b56d984e897a43ba1f403d89e5f4736.png

geometryhexagon