# 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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### How to find a line cuts a circle internally?

I have a circle $S:x^2+y^2=4$ and points $A(2\cos \theta,2\sin \theta)$ and $B(2,0)$ Let $L$ be the tangent to $S$ at $A$. $C$ and $D$ are distinct point on $L$ such that $CA=AD=1$ How can I find ...
1answer
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### How to find area of trapezoid formed from line connecting feet of perpendiculars to angle bisectors?

In $\triangle ABC$, perpendiculars from $A$ to the bisectors of angle $B$ and angle $C$ meet the bisectors in $D$ and $E$, respectively. The line through $D$ and $E$ intersects $AC$ at $X$ and $AB$ at ...
0answers
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### Finding the Angles of a Concylic Quadrilateral

The question is as follows: Let WISH be a cyclic quadrilateral, and K be the intersection of its diagonals WS and HI. Given that arc WI is 100 degrees and arc SH is 80 degrees, find the sizes of ...
1answer
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### A question on properties of triangles.

Find the relation between the circumradius of an obtuse angled triangle and its orthic triangle. I tried using angles in the orthic triangle and sine law but getting stuck. Please help me. Would ...
2answers
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### Functions with other functions as their $x$-axis

I had this interesting thought today as I was playing with making images with mathematical expressions (vector images with graphing if you like) I wanted to to put a spiky thing (the sine curve) ...
0answers
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### Representation of the combination of 2 circles?

I'm creating an iOS app which uses sensor and camera data, combined with GPS data, to determine a specific location for a user. I receive a new GPS location, along with a radius of accuracy, every 10 ...
1answer
121 views

### Average length of a chord in the first quadrant of a circle

One way to calculate it would be doing: $\dfrac{\int_0{}^{r}\int_0{}^{r}\sqrt{(x_1-x_2)^2+(\sqrt{r^2-x_1^2}+\sqrt{r^2-x_2^2})^2} \ \ \ dx_1 \ dx_2}{r^2}$ This seems impossible to integrate it, but ...
1answer
76 views