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Consider three circles \(A\), \(B\) and \(C\), each passing through the points \((-1,0)\) and \((1,0)\). Each circle is cut into three regions by the other two circles. Let ...

If the area ...

True or False?

\(\quad\) There exists a real number \(x\) such that \[x<x^3<x^4<x^2.\]

Two equilateral triangles are joined to create a rhombus. A circle is inscribed so that its center lies on the midpoint of the triangle sides that touch. Two more circles ...

\[\large \begin{cases} x+y=2 \\ xy=4 \\ { S }_{ n }={ x }^{ n }+{ y }^{ n } \end{cases}\] The above equations are given, where \(n\) is a positive integer. It can ...

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