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PR is the diameter of a circle centered on O; its radius AO is the arithmetic mean of a and b. Using the geometric mean theorem, triangle PGR's altitude GQ is the geometric mean. For any ratio a:b, AO ≥ GQ. A semicircle can be used to construct the arithmetic and geometric means of two lengths using straight-edge and compass.
The semi-circle used to visualize the inequalities. When n = 2, the inequalities become + + + for all , >, [3] which can be visualized in a semi-circle whose diameter is [AB] and center D.
Circle-related theory. Apollonius' problem – Geometry problem about finding touching circles Limiting cases of Apollonius' problem – Construct all the circles that are tangent to three given circles; Belt problem – Mathematics problem; Benz plane – Geometrical structure
[25] [26] (Thus, for example, if a square is deformed into a rhombus it remains tangential, though to a smaller incircle). If one side is held in a fixed position, then as the quadrilateral is flexed, the incenter traces out a circle of radius / where a,b,c,d are the sides in sequence and s is the semiperimeter.
The salinon (red) and the circle (blue) have the same area. The salinon (meaning 'salt-cellar' in Greek) is a geometrical figure that consists of four semicircles . It was first introduced in the Book of Lemmas , a work attributed to Archimedes .
Circles G to J, which do not, map to other circles. The reference circle and line L map to themselves. Circles intersect their inverses, if any, on the reference circle. In the SVG file, click or hover over a circle to highlight it. Inversion of a line is a circle containing the center of inversion; or it is the line itself if it contains the ...
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Given three points A, B and C on a circle with center O, the angle ∠ AOC is twice as large as the angle ∠ ABC. A related result to Thales's theorem is the following: If AC is a diameter of a circle, then: If B is inside the circle, then ∠ ABC > 90° If B is on the circle, then ∠ ABC = 90° If B is outside the circle, then ∠ ABC < 90°.
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