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If each semicircle has a diameter equal to 2, what is the length of AD?

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Semicircle AB is flipped upside down and translated horizontally so the new semicircle CD is tangent to AB, as shown. The line through AB is tangent to the semicircle CD and the line through CD is tangent to the semicircle AB.
enter image description here

If each semicircle has a diameter equal to 2, what is the length of AD?
Express your answer in the form √x + √y for positive integers x < y.

posted Oct 4, 2021 by Vikram Luthra

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