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Part of 2021 Novosibirsk Oral Olympiad in Geometry

Problems(2)

angle chasing in ABCD, 80^o, 20^o, 20^o (2021 Novosibirsk Oral Geo Oly 7.2)

Source:

The extensions of two opposite sides of the convex quadrilateral intersect and form an angle of

20^o

, the extensions of the other two sides also intersect and form an angle of

20^o

. It is known that exactly one angle of the quadrilateral is

80^o

. Find all of its other angles.

flags by a robot concyclic, equal angle (2021 Novosibirsk Oral Geo Oly 9.2)

Source:

The robot crawls the meter in a straight line, puts a flag on and turns by an angle

a <180^o

clockwise. After that, everything is repeated. Prove that all flags are on the same circle.

Concyclicgeometry