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Sunday Afternoon Maths XXXVIII

 Posted on 2015-02-01 

Products and sums of squares

Show that the product of any two numbers, each of which is the sum of two square integers, is itself the sum of two square integers.

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Equal side and angle

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

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Arctan

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

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