# Tagged Questions

For questions conserning circles. A circle is a curve composed of points in a plane that are at a fixed distance from a fixed point.

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### How to check if two circles have common part?

I have equasion to calculate area of two circles with common part. Equasion common part But actually I just need to know if two cirlces have common part or no. Is there simpler equasion for that ...
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### Power of a point proof

I found the question on page 13 of this link. Let $P$ be a point inside a circle such that there exist three chords through $P$ of equal length. Prove that $P$ is the center of the circle. I ...
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### Construct a circle passing through a point $X$, which is externally tangent to two given circles

Given two disjoint circles $S_1$ and $S_2$, and a point $X$ external to both of them, is it possible to find the center of a circle that passes through $X$ and touches $S_1$ and $S_2$ tangentially, ...
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### Geometry experts! Three equal tangential circles: What is the ratio of the blue line to the red line?

Consider the three tangential circles of equal radii inscribed in the equliateral triangle (linked to below). What is the ratio of the blue line to the red line? The red line is simply the diameter ...
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### Prove $∠ADM = ∠ACB$ of triangle $ABC$ [closed]

Suppose that $ABC$ is a triangle. Let $D$ be its circumcenter and let $M$ be the midpoint of $\vec {AB}$. Show that $∠ADM = ∠ACB$.
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### point on a circle extract dx and dy?

Given a circle like this, where i know the 2d coordinates of the center, and the radius of the circle, how do i determine the point on the circle, of more precise, dx and dy? illustration Sorry ...
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### Prove a harmonic range from a familiar picture

During solving some simple problem (10th grade), I found this interesting problem, which I got no clue to solve it clean and properly. Hope someone can give me some hint to solve it. Thanks. Given ...
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### Two circles touch internally. Find equation of smaller circle given equation of large circle

A circle C1 has the equation $(x+3)^2 + (y-2)^2 = 25$. Another circle C2 touches the first circle at a point P on the positive y-axis and passes through the centre of C1. The diameter of C1 is twice ...
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### Find the other 2 interior angles of pentagon inscribed in a circle given 3 angles.

Given a pentagon $ABCDE$ inscribed in a circle with centre $O$. Three of the interior angles are $95^°$, $130^°$ and $138^°$. Find angle $x$ and $y$. I'm quite sure that $x$ and $y$ can be found as ...
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### Compute mean on a torus / circular domain

I have $n \in \mathbb{N}$ values lying in a real, circular domain of period $T \in \mathbb{R}^{+*}$: $(\xi_i \in [0, T[^c)_{i \in \{1,\dots, n\}}$ I refer to the domain $C_T = [0, T[^c$ as a "...
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### Drawing a straight line, and then curving along a circle

I am primarily a programmer, one with unfortunately relatively little education in mathematics, but I always try to get by. Right now, I am working with a simple set of rules. Draw a straight line in ...
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### Prove that the center of a circle within a constructed triangles lies on the angle bisector

I was given steps to construct a figure: 1.) Construct a horizontal ray AB and a segment AC at an angle to the ray. Locate point D anywhere on ray AB and construct the segment CD. 2.) Construct the ...
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I know the radius $R$ of the circle and the area $A$ of the segment. How can I solve for central angle $\alpha^{\circ}$ in this (or some other) equation: $$A=\frac{R^{2}}{2} \left( \frac{\alpha \pi}{... 1answer 91 views ### Relationship between incenter and circumcenter Let ABC be an acute triangle with circumcenter O and incenter I. Points E, M lie on AC and F, N on AB so that BE ⊥ AC, CF ⊥ AB, ∠ABM = ∠CBM and ∠ACN = ∠BCN. Prove that I lies on EF if and only if O ... 2answers 39 views ### How to determine the angle of intersection? (2 circles) Here's an example of what I have: The radius of both circles is 50. Each circle is moved in by 10, so the distance between the two center points is 80. As you can see one of the circles end at 90 ... 2answers 45 views ### Finding sides of triangle Given :$$\triangle ABCM \in AB,N \in BC ,P \in AC$$are the points at which the incircle crosses the triangle$$MN=3\sqrt{10}NP=2\sqrt{20}PM=10 I have to find the sides of the ...
I have a line which is divided into small segments. In the following diagram we have the first segment defined by two points $P_1$ and $P_2$. However, imagine the line having other segments evenly ...