Circles and Triangles
Regular readers will know that I love a good puzzle. I love all maths problems, but ones which make me think and get me stuck a bit are by far my favourite. The other day Ed Southall (@solvemymaths) shared this little beauty that did just that:
I thought “Circles and a 3 4 5 triangle – what an awesome puzzle”, I reached for a pen an paper and drew out the puzzle.
I was at a bit of a loss to start with. I did some pythag to work some things out:
Eliminated y and did some algebra:
Wrote out what I knew:
And drew a diagram that didn’t help much:
I then added some additional lines to my original diagram:
Which made me see what I needed to do!
I redrew the important bits (using the knowledge that radii meet tangents at 90 degrees and that the line was 3.2 away from c but the center of the large circle was 2.5 away):
Then considered the left bit first:
Used Pythagoras’s theorem:
Then solved for x:
Then briefly git annoyed at myself because I’d already used x for something else.
I did the same with the other side to find the final radius.
I hope you enjoyed this one as much as I did!