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Math Question

The figure shows two semicircles with centers \( P \) and \( M \). The semicircles are tangent to each other at point \( B \), and \( \frac{D E}{D E} \) is tangent to both semicircles at \( F \) and \( E \).
If \( P B=B C=6 \), what is \( E D ? \)
(A) 6
(B) \( \sqrt{48} \)
(C) 8
(D) \( \sqrt{72} \)

Solution

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