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angle, ratio 2:1, 1:1 by orhocenter (IV Soros Olympiad 1997-98 R2 9.3)

Source:

June 1, 2024

ratiogeometryorthocenterangles

Problem Statement

What is angle

B

of triangle

ABC

, if it is known that the altitudes drawn from

A

and

C

intersect inside the triangle and one of them is divided by of intersection point into equal parts, and the other one in the ratio of

2: 1

, counting from the vertex?