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.

Read more about Malfatti Circles: Malfatti's Problem, History, Steiner's Construction, Radius Formula, Ajima–Malfatti Points

### 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 ...

**Malfatti Circles**- Ajima–Malfatti Points

... 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 ...

### Famous quotes containing the word circles:

“By the power elite, we refer to those political, economic, and military *circles* which as an intricate set of overlapping cliques share decisions having at least national consequences. In so far as national events are decided, the power elite are those who decide them.”

—C. Wright Mills (1916–1962)