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.
Read more about this topic: Inscribed Figure
Famous quotes containing the words facts, inscribed and/or figures:
“Is it true or false that Belfast is north of London? That the galaxy is the shape of a fried egg? That Beethoven was a drunkard? That Wellington won the battle of Waterloo? There are various degrees and dimensions of success in making statements: the statements fit the facts always more or less loosely, in different ways on different occasions for different intents and purposes.”
—J.L. (John Langshaw)
“Farewell sadness
Good-day sadness
You are inscribed in the lines of the ceiling.”
—Paul Éluard (1895–1952)
“But that wasn’t fancy enough for Lord Byron, oh dear me no, he had to invent a lot of figures of speech and then interpolate them,
With the result that whenever you mention Old Testament soldiers to
people they say Oh yes, they’re the ones that a lot of wolves dressed up in gold and purple ate them.”
—Ogden Nash (1902–1971)