#Geometry/logic olympiad question

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feral canyon
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"The figure shows a large square divided into 4 smaller squares and an internal circle that is tangent to the large square at the midpoint of one of its sides. How long are the sides of the large square?"

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feral canyon
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I have no idea how to even start

vagrant forum
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slope intercept method

feral canyon
vagrant forum
ocean idol
ocean idol
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ocean idol
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I mistakenly wrote -ve sign instead of +ve on this line:
$CD = BD - CB = a - (a-4) (+) \sqrt{(a-4)^2 - (a-6)^2}$

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Bocchi