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# Shape and Territory

If for a triangle $ABC$

what can you say about the triangle?

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### Fixing It

### OK! Now Prove It

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Age 16 to 18

Challenge Level

If for a triangle $ABC$

$\tan(A - B) + \tan(B - C) +
\tan(C - A) = 0$

what can you say about the triangle?

A and B are two fixed points on a circle and RS is a variable diamater. What is the locus of the intersection P of AR and BS?

Make a conjecture about the sum of the squares of the odd positive integers. Can you prove it?