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4

Part of 2022 Oral Moscow Geometry Olympiad

Problems(2)

CK _|_ A'B' wanted, <BAC =60^o

Source: 2022 Oral Moscow Geometry Olympiad grades 8-9 p4

4/17/2022
In triangle ABCABC, angle CC is equal to 60o60^o. Bisectors AA′AA' and BB′BB' intersect at point II. Point KK is symmetric to II with respect to line ABAB. Prove that lines CKCK and A′B′A'B' are perpendicular.
(D. Shvetsov, A. Zaslavsky)
perpendicularityperpendiculargeometry
orthocenter construction using a ruler at most with 6 lines

Source: 2022 Oral Moscow Geometry Olympiad grades 10-11 p4

4/18/2022
An acute-angled non-isosceles triangle ABCABC is drawn, a circumscribed circle and its center OO are drawn. The midpoint of side ABAB is also marked. Using only a ruler (no divisions), construct the triangle's orthocenter by drawing no more than 66 lines.
(Yu. Blinkov)
geometryconstructionorthocenterRuler