Tangent Circles
In 1822 Karl Feuerbach discovered that any triangle's nine-point circle is externally tangent to that triangle's three excircles and internally tangent to its incircle; this result is known as Feuerbach's theorem. He postulated that:
- ... the circle which passes through the feet of the altitudes of a triangle is tangent to all four circles which in turn are tangent to the three sides of the triangle... (Feuerbach 1822)
The point at which the incircle and the nine-point circle touch is often referred to as the Feuerbach point.
Read more about this topic: Nine-point Circle
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