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The above diagram shows \(8\) circles. The yellow and green circles are concentric, with the radius of the green circle being \(1\) unit and the radius of the yellow circle ...

Find the minimum positive integral value of \(n\) such that there exist \(n\) points in \(\mathbb{R}^3\) with the property that there exist exactly \(12\) distinct pairs of points ...

Let \(ABCD\) be a square with points \(E\) and \(F\) on \(CD\) and \(BC,\) respectively, such that \(AE \perp EF, AE=4,\) and \(EF=3.\)

If the area of ...

The five sides and five diagonals of a regular pentagon are drawn on a piece of paper. CJ and Dan play a game in which they take turns to color ...

Let \(\{a_i\}_{i=1}^n\) be a sequence of positive reals such that \(a_1+a_2+\cdots +a_n=n\), where \(n\) is a positive integer. Find the smallest value of ...

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