Browsing category circles

Ask Uncle Colin: Circles

Dear Uncle Colin, I’m told there are two circles that touch the x-axis at the origin and are also tangent to the line $4x-3y+24=0$, but I can’t find their equations. Any ideas? - A Geometrically Nasty Example Seems Impossible Hi, AGNESI, and thanks for your message! I’m going to start

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Ask Uncle Colin: Trouble in Sector ABC

Dear Uncle Colin, I got stuck on this sector question, which asks for the radius of circle $P$, which touches sector $ABC$ as shown. I'm given that $ABC$ is a sector of a circle with centre $A$ with radius 12cm, and that angle $BAC$ is $\frac{\pi}{3}$. My answer was 3.8cm,

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Ask Uncle Colin: Find me a circle!

Dear Uncle Colin, I have two points and I want to construct a circle of a given radius that passes through them. Is it possible? -- Every Underspecified Circle Lives Its Dream Hi, EUCLID, and thanks for your message! There are three possible answers to this, depending on the size

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A MathsJam Masterclass: A Circle That Won’t Behave

Somewhere deep in the recesses of my email folder lurks a puzzle that looks simple enough, but that several of my so-inclined friends haven't found easy: A circle of radius $r$, has centre $C\ (0,r)$. A tangent to the circle touches the axes at $A\ (9,0)$ and $B\ (0, 2r+3)$.

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Ask Uncle Colin: how do you find the intersection of three circles?

Dear Uncle Colin, I've been challenged to find the area of the intersection of three circles while drawing a Venn diagram. I don't know where to start!-- Triangle Unpredictably Rounded; I'm No Genius For a moment, TURING, I thought there wasn't a problem in this problem, but then I realised:

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How the Mathematical Ninja explains the Mathematical Pirate’s circle trick

"Let me see that!" commanded the Mathematical Ninja, looking at one of the Mathematical Pirate's blog posts. "That's... but that's..." "It's not wrong!" said the Mathematical Pirate, smugly. "It just works!" "But you're presenting it as magic, not as maths." The Mathematical Pirate nodded eagerly. "Lovely magic! How does it

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How the Mathematical Pirate finds the centre and radius of a circle

"Arr?" said the student, really not sure. "No, no, $r$," said the Mathematical Pirate. "The centre is at C -- or $(a,\, b)$, if you prefer -- and the radius is $r$." "Gotcha. So, if you've got something like $x^2 + y^2 + 8x - 12y + 3=0$, how do

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A circle problem that succumbs to a circle theorem

A tweet from @GregSchwanbeck some time back asked: Does square or circle have greater perimeter? A surprisingly hard prob for HS: #mathchat #math — Greg Schwanbeck (@GregSchwanbeck) March 16, 2015 The setup is: one side of a square is tangent to a circle, and two corners of the

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Minecraft circles

I have a confession to make. One that will lower me seriously in the esteem of my 10-year-old nephew: I don't really get Minecraft. Sorry, buddy. I've tried it. I love that you love it -- honestly, creative games are awesome for your problem-solving skills and breaking down the barriers

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How I approximated $\pi$ for “Pi Day”

There was a post here, but it's not here any more! Instead, it's over at the Aperiodical, as part of their $\pi$ Day approximation challenge.

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