In geometry, the Malfatti circles are three circles inside a given triangle such that each circle is tangent to the other two and to two sides of the triangle. They are named after Gian Francesco Malfatti, who made early studies of the problem of constructing these circles in the mistaken belief that they would have the largest possible total area of any three disjoint circles within the triangle. Malfatti's problem has been used to refer both to the problem of constructing the Malfatti circles and to the problem of finding three area-maximizing circles within a triangle.
Other articles related to "malfatti, circles, malfatti circles, circle":
... In 1803, Gian Francesco Malfatti proved that a certain arrangement of three circles would cover the maximum possible area inside a right triangle ... assumptions about the configuration of the circles ... It was shown in 1930 that circles in a different configuration could cover a greater area, and in 1967 that Malfatti's configuration was never optimal ...
... Given a triangle ABC and its three Malfatti circles, let D, E, and F be the points where two of the circles touch each other, opposite vertices A, B, and C respectively ... AD, BE, and CF meet in a single triangle center known as the first Ajima–Malfatti point after the contributions of Ajima and Malfatti to the circle problem ... The second Ajima–Malfatti point is the meeting point of three lines connecting the tangencies of the Malfatti circles with the centers of the excircles of the triangle ...
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