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angle wanted, 1 circles and 3 lines (II Soros Olympiad 1995-96 R1 9.3)

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June 2, 2024
geometryangles

Problem Statement

Two straight lines are drawn on a plane, intersecting at an angle of 40o40^o. A circle with center at point OO touches these lines. Let's consider a line, different from the given ones, tangent to the same circle and intersecting the given lines at points BB and CC. What can the angle ∠BOC\angle BOC be equal to?
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