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If you want to find similar triangles, use only SSS, SAS and AAA. Don't make an ASS of yourself.

\(ABCD\) is a square with \(AB=13\). Points \(E\) and \(F\) are exterior to \(ABCD\) such that \(BE=DF=5\) and \(AE=CF=12\).

If the length of \(EF\) can be represented as \(a\sqrt b \) where \(a\) and \(b\) are positive integers and \(b\) is not divisible by the square of any prime, then find \(ab\).

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The area of the largest square which can be inscribed in a triangle with side lengths \(3, 4, 5\) is \(\dfrac{a}{b}\).

Find \(a+b\), where \(a\) and \(b\) are coprime, positive integers.

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\(BCDF\) is a rectangle. Triangle \(ABE \) has an area of \( 2 \text{ cm}^2 \). Triangle \(BEF \) has an area of \( 3 \text{ cm}^2 \).

Find the area of the blue region (in \( \text{cm} ^2 \)). Give your answer to 1 decimal place.

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If triangle \(ABC\) is similar to triangle \(BFA,\) then find \(\dfrac{AB}{BC}.\)

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There is a common tangent which intersects the three tangent circles shown above at \(E,\) \(F,\) and \(G.\) If \( EF = 6 \) and \( FG = 3 \), find the area of the orange region. Use the approximation \(\pi \approx \frac{22}{7}.\)

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