Day 2 with a neat geometry puzzle that Catriona Agg shared

Yesterday we did a project on this geometry problem shared by Catriona Agg:

In a @MathsHubs meeting today, we were given this to ponder over lunch: how many interesting solutions can you come up with?

Lunch break was just long enough for me to teach Y13, so I gave it to them. I had 3 solutions, they gave me 2 more – one of which is my favourite by far. pic.twitter.com/Wu6XB91b4m

— Catriona Agg (@Cshearer41) November 6, 2020

I also shared the problem on Facebook and a friend from college shared a solution that I’d not seen before (though looking back at Catriona’s twitter thread, it is there . . . . of course!). So, today I decided to take a 2nd day with the problem and have my son look at this new solution.

But I started by having him explain the “power of point” solution I shared with him yesterday just to get warmed up:

Next I set up my friend Raf’s solution to see if my son could solve the problem using this clever idea:

Finally, since the solution with the full inscribed circle depends on a geometry formula relating the area and perimeter of a triangle to the length of the radius of the inscribed circle, I asked my son if he could prove that formula was true. It took him a minute to find the idea, but he was able to construct the proof:

I was happy to be able to share three different solutions to the problem that Catriona shared. It definitely made for a fun little weekend geometry review!

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