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Try a numerical example, say the 3 points give a triangle of sides 12, 15 and 13. Find the radii of the circles.
Now use the same method if the sides of the triangle are $a$, $b$ and $c$?
Generalise still more: What about 4 circles? 5 circles? $n$ circles?
Polycircles
Age 14 to 16
Challenge Level 
Try a numerical example, say the 3 points give a triangle of sides 12, 15 and 13. Find the radii of the circles.
Now use the same method if the sides of the triangle are $a$, $b$ and $c$?
Generalise still more: What about 4 circles? 5 circles? $n$ circles?
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A group of 20 people pay a total of £20 to see an exhibition. The admission price is £3 for men, £2 for women and 50p for children. How many men, women and children are there in the group?
