The figure shows a scalene triangle ABC with
the circumcircle of center O and angle B = 60 degrees. The Euler line OH intersects
arc AB, AB, BC, and arc BC at C2, C1, A1, and A2,
respectively. Prove that (1) OH = C1C2 - A1A2;
(2) OH = AC1 - CA1; (3) OH = AB - BC; (4) OC1
= HA1.
![Geometry Problem 1062 Scalene Triangle with an angle of 60 degrees, Euler Line, Orthocenter, Circumcenter, Distance, Congruence, Transversal Infographic Geometry problem: Scalene Triangle with an angle of 60 degrees, Euler Line, Orthocenter, Circumcenter, Distance, Congruence](p1062-triangle-60-degrees-euler-line-circumcircle-distance-math.gif)
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