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Calculate the value of AN

Source: Brazil Undergrad MO - Galois-Noether 2018 #17

November 26, 2019
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Problem Statement

In the figure, a semicircle is folded along the AN AN string and intersects the MN MN diameter in B B . MB:BN=2:3 MB: BN = 2: 3 and MN=10 MN = 10 are known to be. If AN=x AN = x , what is the value of x2 x ^ 2 ?
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