6-447: (Redirected from Power Center ) Power center may refer to: Power center (geometry) , the intersection point of the three radical axes of the pairs of circles Power center (retail) , an unenclosed shopping center with 250,000 square feet (23,000 m) to 750,000 square feet (70,000 m) of gross leasable area See also [ edit ] Power station Topics referred to by
12-447: Is different from Wikidata All article disambiguation pages All disambiguation pages Power center (geometry) In geometry , the power center of three circles , also called the radical center , is the intersection point of the three radical axes of the pairs of circles. If the radical center lies outside of all three circles, then it is the center of the unique circle (the radical circle ) that intersects
18-417: 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 . Therefore, at the intersection point of these two lines , all three powers must be equal, h 1 = h 2 = h 3 . Since this implies that h 1 = h 3 , this point must also lie on
24-444: The radical axis of circles 1 and 3. Hence, all three radical axes pass through the same point, the radical center. The radical center has several applications in geometry. It has an important role in a solution to Apollonius' problem published by Joseph Diaz Gergonne in 1814. In the power diagram of a system of circles, all of the vertices of the diagram are located at radical centers of triples of circles. The Spieker center of
30-421: The same term [REDACTED] This disambiguation page lists articles associated with the title Power center . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=Power_center&oldid=1137711556 " Category : Disambiguation pages Hidden categories: Short description
36-432: The three given circles orthogonally ; the construction of this orthogonal circle corresponds to Monge's problem . This is a special case of the three conics theorem . The three radical axes meet in a single point, the radical center, for the following reason. 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
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