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# Puzzles

## Archive

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## Cutting corners

The diagram below shows a triangle $$ABC$$. The line $$CE$$ is perpendicular to $$AB$$ and the line $$AD$$ is perpedicular to $$BC$$.
The side $$AC$$ is 6.5cm long and the lines $$CE$$ and $$AD$$ are 5.6cm and 6.0cm respectively.
How long are the other two sides of the triangle?

## Equal side and angle

In the diagram shown, the lengths $$AD = CD$$ and the angles $$ABD=CBD$$.
Prove that the lengths $$AB=BC$$.

## Arctan

Prove that $$\arctan(1)+\arctan(2)+\arctan(3)=\pi$$.