# Questions tagged [circles]

For questions concerning circles. A circle is the locus of points in a plane that are at a fixed distance from a fixed point.

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### The locus of points of the form $ae^{i\theta}+be^{i\phi}$

Let $a$ and $b\in\mathbb{R}^{>0}$ be two positive real numbers. What is the locus of points of the form $ae^{i\theta}+be^{i\phi}$ where $\theta$ and $\phi\in[-\pi,\pi)$? Does it have any specific ...
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### Prove that A₁D, B₁E, C₁F intersect at the same point

Let ABC be a triangle.AA₁, BB₁, CC₁ are the angle bisectors of the triangle. ω is circumcircle of ABC. ω∩AA₁=A₂, ω∩BB₁=B₂, ω∩CC₁=C₂. Circumcircles of AB₁B₂, BC₁C₂, CA₁A₂ intersect with AB,BC and CA at ...
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### Tantalising Geometry!

A triangle with side lengths $5$, $6$ and $9$ has a circle inscribed IN IT! (ignore the wording below) What is the radius of the circle? I'm not sure where to start and, as well as hints/an answer, ...
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### Minimize area of n-gon circumscribed around unit circle

Given regular unit circle and a n-gon, circumscribed around this unit circle. I need to minimize area of n-gon. Also i need to find the limit of n-gon area with $n\rightarrow \infty$. Intuitively i ...
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### What is the size of each side of the square?

The diagram shows 12 small circles of radius 1 and a large circle, inside a square. Each side of the square is a tangent to the large circle and four of the small circles. Each small circle touches ...
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### Can arc be measured by degree? [closed]

I saw a math problem that says the measure of an arc of a circle is $40^\circ$. My question is how can an arc be measured by degree? What is it called? Please make me understand.
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### Prove that A(FKP)=A(EDP).

ABCD is circumcircled in W. It is trapezoid. Mid points of parallel sides, BC and AD are E and F respectively. AB and DC intersect at P, W(circle) and BF intersect at K. Then prove A(FKP)=A(EDP) Where ...
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### Tangent to the circle concentric with the circle, $2x^2+2y^2-6x-10y=183$
Let $C$ be the circle concentric with the circle, $2x^2+2y^2-6x-10y=183$ and having area $(1/10)th$ of the area of this circle. Then a tangent to $C$, parallel to the line, $3x+y=0$ makes an intercept ...