Facts About Inscribed Figures
- Every circle has an inscribed triangle with any three given angle measures (summing of course to 180°), and every triangle can be inscribed in some circle (which is called its circumscribed circle).
- Every triangle has an inscribed circle, called the incircle.
- Every circle has an inscribed regular polygon of n sides, for any n≥3, and every regular polygon can be inscribed in some circle.
- Every regular polygon has an inscribed circle, and every circle can be inscribed in some regular polygon of n sides, for any n≥3.
- Every triangle has an infinitude of inscribed ellipses. One of them is a circle, and one of them is the Steiner inellipse which is tangent to the triangle at the midpoints of the sides.
- Every triangle has three inscribed squares, though two of them coincide with each other in the case of a right triangle.
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