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The radical axis of a pair of circles is defined as the set of points that have equal power h with respect to both circles. For example, for every point P on the radical axis of circles 1 and 2, the powers to each circle are equal: h 1 = h 2. Similarly, for every point on the radical axis of circles 2 and 3, the powers must be equal, h 2 = h 3.
If the radii are equal, the radical axis is the line segment bisector of M 1, M 2. In any case the radical axis is a line perpendicular to ¯. On notations. The notation radical axis was used by the French mathematician M. Chasles as axe radical. [1] J.V. Poncelet used chorde ideale. [2]
Spherical version of Malfatti's problem: [4] The triangle is a spherical one. Essential tools for investigations on circles are the radical axis of two circles and the radical center of three circles. The power diagram of a set of circles divides the plane into regions within which the circle minimizing the power is constant.
The radical axis of two intersecting circles. The power diagram of the two circles is the partition of the plane into two halfplanes formed by this line. In the case n = 2, the power diagram consists of two halfplanes, separated by a line called the radical axis or chordale of the two circles. Along the radical axis, both circles have equal power.
For instance, if the one solving the math word problem has a limited understanding of the language (English, Spanish, etc.) they are more likely to not understand what the problem is even asking. In Example 1 (above), if one does not comprehend the definition of the word "spent," they will misunderstand the entire purpose of the word problem.
A pencil of circles (or coaxial system) is the set of all circles in the plane with the same radical axis. [9] To be inclusive, concentric circles are said to have the line at infinity as a radical axis. There are five types of pencils of circles, [10] the two families of Apollonian circles in the illustration above represent two of them.