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# Congruent and Similar Triangles

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

# Congruent and Similar Triangles: Level 3 Challenges

$$ABCD$$ 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 $$ab$$.

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.

$$BCDF$$ 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.

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

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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