Auxiliary circle
Overview
Important
An auxiliary circle is a circle that is drawn in a geometric problem to help solve it, even though it is not part of the original figure. In triangle geometry, the most common auxiliary circle is the circumcircle, which passes through all three vertices of a triangle. Auxiliary circles can help reveal hidden relationships, such as equal angles or lengths, or help construct points with special properties.
Important properties
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Auxiliary circles are not part of the original problem but are added to make solving easier.
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They can help identify cyclic quadrilaterals, equal angles, or similar triangles.
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The circumcircle of a triangle is a common example of an auxiliary circle.
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Auxiliary circles can be used to prove properties about tangents, chords, and intersections.