# Browsing category geometry

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

## A proof without words

Via nRICH: A circle touches the lines OA extended, OB extended and AB where OA and OB are perpendicular. Show that the diameter of the circle is equal to the perimeter of the triangle. $\blacksquare$

## A Catriona Shearer Classic

If you’ve read this blog for a while, you’ll know I’m a fan of @cshearer41’s puzzles (her book, Geometry Puzzles in Felt Tip, is available wherever etc). At a recent MathsJam, one jumped out of Chalkdust at us: (Image from Issue 10 of Chalkdust, a magazine for the mathematically curious.)

## Eye to Eye

A nice observation from Futility Closet: Draw two circles of any size and bracket them with tangents, as shown. The chords in blue will always be equal. I’m hardly going to let that pass by without a proof, now, am I? Spoilers below the line. My proof Definitions Let the

## Some puzzles from Cav

A couple of puzzles that came my way via @srcav today: Cav’s solutions to this one are here; mine are below the line further down. Interesting angle puzzle https://t.co/UN13XwwY3o pic.twitter.com/NyaQL0H7wE — Cav (@srcav) July 8, 2019 And to this one, here Have a go yourself before you read on! I’ve

## A Tenth Of A Pizza

On Twitter, @Trianglemanscd posed a pertinent problem: Making pizzas tonight but cannot recall how to cut them in 10 slices. — Christopher Danielson (@Trianglemancsd) May 31, 2019 Stand back everyone! I have compasses and a straight-edge and I’m not afraid to use them; the Geogebra demonstration below shows one way

## Barney’s triangles

A puzzle from @Barney_MT: Find angle BDC This turns out to be a bit more demanding than I expected. There are spoilers below the line, showing a solution that took rather more time and space than the final polished version does. Spoilers below the line! Adding in circles When I’ve

## Barney’s Wedge

Once upon a MathsJam, Barney Maunder-Taylor showed up with a curious object, a wedge with a circular base. Why? Well, if you held a light above it, it cast a circular shadow. From one side, the shadow was an equilateral triangle; along the third axis, a rectangle. A lovely thing.

## Regions of a circle

On a recent MathsJam Shout, an Old Chestnut appeared (in this form, due to @jamestanton): If you’ve not seen it, stop reading here and have a play with it - it’s a classic puzzle for a reason. Below the line are spoilers. Counting is hard The first thing you’d probably

## Futility Closet, Fibonacci and Quadratic Residues

I love Futility Closet -- it's an incredible collection of interesting bits and pieces, but it has a special place in my heart because they love and appreciate maths. Not only that, they appreciate maths that I find interesting. The internet has many interesting miscellanies, and many excellent sites specialising