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The circle is an instance of a conic section and the nine-point circle is an instance of the general nine-point conic that has been constructed with relation to a triangle ABC and a fourth point P, where the particular nine-point circle instance arises when P is the orthocenter of ABC.
The nine-point circle passes through these three midpoints; thus, it is the circumcircle of the medial triangle. These two circles meet in a single point, where they are tangent to each other. That point of tangency is the Feuerbach point of the triangle. Associated with the incircle of a triangle are three more circles, the excircles. These ...
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Circle theorem may refer to: Any of many theorems related to the circle; often taught as a group in GCSE mathematics. These include: Inscribed angle theorem. Thales' theorem, if A, B and C are points on a circle where the line AC is a diameter of the circle, then the angle ∠ABC is a right angle. Alternate segment theorem. Ptolemy's theorem.
Haboush's theorem (algebraic groups, representation theory, invariant theory) Hadamard three-circle theorem (complex analysis) Hadamard three-lines theorem (complex analysis) Hadwiger's theorem (geometry, measure theory) Hahn decomposition theorem (measure theory) Hahn embedding theorem (ordered groups) Hairy ball theorem (algebraic topology)
The second theorem considers five circles in general position passing through a single point M. Each subset of four circles defines a new point P according to the first theorem. Then these five points all lie on a single circle C. The third theorem considers six circles in general position that pass through a single point M. Each subset of five ...
Jack Nicholson spent some quality time with his loved ones over the holiday season.. In an Instagram post shared by his daughter Lorraine Nicholson on Thursday, Jan. 2, the actor, 87, was captured ...
A circle is tangent to a point if it passes through the point, and tangent to a line if they intersect at a single point P or if the line is perpendicular to a radius drawn from the circle's center to P. Circles tangent to two given points must lie on the perpendicular bisector. Circles tangent to two given lines must lie on the angle bisector.