A triangle has sides 12, 13 and 15 units. Circles are drawn with centres at the vertices of the triangle so that each circle touches the other two.
Find the radii of the circles.
Can you always find touching circles for any triangle?
What similarities and differences can you see between Polycircles, The Checkit Game with Addition https://aiminghigh.aimssec.ac.za/checkit-game/ and The Triangle Midpoints Problem https://aiminghigh.aimssec.ac.za/triangle-midpoints/?
This problem is adapted from the NRICH task Polycircles with permission of the University of Cambridge. All rights reserved.