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The nine-point circles are all congruent with a radius of half that of the cyclic quadrilateral's circumcircle. The nine-point circles form a set of four Johnson circles. Consequently, the four nine-point centers are cyclic and lie on a circle congruent to the four nine-point circles that is centered at the anticenter of the cyclic quadrilateral.
The equator, a circle of latitude that divides a spheroid, such as Earth, into the northern and southern hemispheres. On Earth, it is an imaginary line located at 0 degrees latitude . 0°
For promotion from Secondary level (Class IX-X) to Senior Secondary level (Class XI-XII), a student must obtain, for all subjects (or best 5 if 6 subjects are taken), 33% overall, without any minimum theory mark requirement. Originally, the passing criteria were set such that a student had to get 33% in both the theory and practical components.
For three circles denoted by C 1, C 2, and C 3, there are three pairs of circles (C 1 C 2, C 2 C 3, and C 1 C 3). Since each pair of circles has two homothetic centers, there are six homothetic centers altogether. Gaspard Monge showed in the early 19th century that these six points lie on four lines, each line having three collinear points.
The "nine dots" puzzle. The puzzle asks to link all nine dots using four straight lines or fewer, without lifting the pen. The nine dots puzzle is a mathematical puzzle whose task is to connect nine squarely arranged points with a pen by four (or fewer) straight lines without lifting the pen.
The two given circles α and β touch the n circles of the Steiner chain, but each circle C k of a Steiner chain touches only four circles: α, β, and its two neighbors, C k−1 and C k+1. By default, Steiner chains are assumed to be closed , i.e., the first and last circles are tangent to one another.
The osculating circle to the curve is centered at the centre of curvature. Cauchy defined the center of curvature C as the intersection point of two infinitely close normal lines to the curve. [1] The locus of centers of curvature for each point on the curve comprise the evolute of the curve.
A math circle is an extracurricular activity intended to enrich students' understanding of mathematics. The concept of math circle came into being in the erstwhile USSR and Bulgaria , around 1907, with the very successful mission to "discover future mathematicians and scientists and to train them from the earliest possible age".