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In which figure is the black path the shortest?

Difficulty: slightly spicy 🌶🌶🌶

This problem gets two chili peppers because there are some quick-and-clever solutions where the path lengths are carefully ...

If the purple area is \(A \pi,\) what is \(A?\)

Note that the figure shows 2 semicircles whose diameters lie on a common line. The chord \( DE \) of the larger ...

\[\dfrac{a+b}{c} = \dfrac{a}{c} + \dfrac{b}{c} \]

We know that we can split a fraction like what we did above, but you can't do this in ...

Which is larger: the yellow area or the blue area?

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