Tagged Questions

Questions on the circle, a curve composed of points in a plane that are at a fixed distance from a fixed point.

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Prove that these 3 points are in a straight line.

A triangle ABC is inscribed in a circle $\omega$. $BB_1$ bisects $\angle ABC$ (and so $M$ is the midpoint of the arc $AC$ ($B \notin AC$, where $AC$ is the arc)). $B_1K \perp BC$ ($K\in\omega$). ...
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Length of hypotenuse

Let a circle centered at $O$ have radius $OA=10$. Let OB be perpendicular on OA.Let G and E be points respectively on on OB and OA.Let F be a point on the circumference such that GFEO is a ...
550 views

Find a circle orthogonal to two other circles

Given two circles $x^2+(y-4)^2=4^2$ and $(x-8)^2+(y+2)^2=2^2$ I need to find the circle that's orthogonal to both the above circles, and contains the point $P=(8,4).$ Is there an algebraic way ...
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Finding the equation of a circle from given points on it and line on which the centre lies.

What are some effective ways to find the equation of a circle when you are given points lying on the circle and the equation for the line on which the centre of the circle lies. Here is an example of ...
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Computing a matrix to convert an (x,y) point on an ellipse to a circle

I have an ellipse defined by its semi-major axis, inclination, and position angle. The ellipse is centered on the origin. I would like to solve for a matrix that converts this ellipse to a circle. ...
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Calculating the Apollonius Circle

This is a followup to a question I asked earlier. I have looked for an example on Google and StackExchange, but I have yet to see a clear example of the formula to determine the equation of an ...
831 views

Area of intersection between 4 circles centered at the vertices of a square

The centers of four circles are at the vertices of a square of sidelength 100m. Each circle has the radius of 100m. Which is the area of their intersection?
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Prove that a circle has an infinite number of tangents

It seems obvious that a circle is comprised of the set of all points that are equidistant from one point, and that each point on the circumference of the circle represents a tangent. This seems to ...
264 views

Infinite series of tangential circles?

I want to show that for all $n$ there is some collection of $n + 2$ circles such that two of the circles ($A$ and $B$) are tangential to each of the remaining $n$ circles (but not to each other) and ...
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Can we prove that circle has at most two colinear points?

Ok so I stumbled across a problem(I found a solution just to be clear) and it got me thinking.The problem is a classic,it was challenge to prove that line can intersect circle in at most 2 points. So ...
The circle $C: x^2 + y^2 + kx + (1+k)y - (k+1)=0$ passes through two fixed points for every real number $k$. Find $(i)$ co-ordinates of these two points and $(ii)$ the minimum value of the radius.