MathDB

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Part of 2022 Novosibirsk Oral Olympiad in Geometry

Problems(3)

<B=? if <C = 3<A and AB=2 BC (2022 Novosibirsk Oral Geo Oly 8.4)

Source:

9/2/2023
In triangle ABCABC, angle CC is three times the angle AA, and side ABAB is twice the side BCBC. What can be the angle ABCABC?
geometryangles
rectangle by 7 corners (2022 Novosibirsk Oral Geo Oly 7.4 8.3)

Source:

9/2/2023
Fold the next seven corners into a rectangle. https://cdn.artofproblemsolving.com/attachments/b/b/2b8b9d6d4b72024996a66d41f865afb91bb9b7.png
geometryrectangle
incenter of BCD lies on circumcenter of ABD (2022 Novosibirsk Oral Geo Oly 9.4)

Source:

9/3/2023
A point DD is marked on the side ACAC of triangle ABCABC. The circumscribed circle of triangle ABDABD passes through the center of the inscribed circle of triangle BCDBCD. Find ∠ACB\angle ACB if ∠ABC=40o\angle ABC = 40^o.
geometryincentercircumcircle