# Questions tagged [circles]

For elementary questions concerning circles (or disks). A circle is the locus of points in a plane that are at a fixed distance from a fixed point. Use this tag alongside [geometry], [Euclidean geometry], or something similar. Do not use this tag for more advanced topics, such as complex analysis or topology.

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### Finding the circumradius of a cyclic hexagon, given three non-consecutive sides and the fact that the midpoints of all sides are also cyclic

Cruel Geometry Question, Mock AIME-i 2015: Let $A_1A_2A_3A_4A_5A_6$ be a hexagon inscribed inside a circle of radius $r$. Furthermore, for each positive integer $1 \leq i \leq 6$ let $M_i$ be the ...
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### Sangaku problem about three chords in a circle

Inside circle $O$ (shown with white interior), a blue circle sits at the bottom. $O$ has two chords that meet at the top of $O$ and are tangent to the blue circle. $O$ also has a horizontal chord ...
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### Parametric Equation of a unit circle when the angle between $x$-axis and $y$-axis is not $90$ degrees

I know in regular Cartesian coordinates the parametric equation for a unit circle is $x=\cos(\theta)$, $y=\sin(\theta)$, and if the $x$ coordinates are stretched by an amount $a$, and the $y$ ...
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### Sangaku problem: Show that five circles have equal radii.

Inspired by Sangaku problems such as these, I created the following Sangaku problem. Consider the following diagram. Description: The diagram shows the circle $x^2+y^2=1$, two red chords with ...
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### Question on circle and binomial coefficient [duplicate]

On a circle C, put n points on the circumference of C. Now the question says that 𝐶ₙ is the number of chords (such that no 3 chords intersect at any one point), 𝑖ₙ that of intersections of chords ...
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### I need help in understanding the alternative solution provided to solve this geometry question of calculating area of quadrilateral

Question: Solution provided: I understand this part that equal chords of a circle subtend equal angles at the center, but after this the faculty transformed this whole diagram to one shown below in ...
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### A circle is inscribed in a triangle, with three other circles in the corner regions. The radii are integers. Possible values of the largest radius?

Consider four circles with integer radii inscribed in a triangle as shown. That is, a circle with integer radius $R$ is inscribed in a triangle, and three other circles with integer radii $a,b,c$ are ...
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