# Find The Length

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Let $$A$$ and $$B$$ be two distinct points on a circle $$\Gamma$$ that are not diametrically opposite. Let $$B'$$ be the diametrically opposite point of $$B$$ on $$\Gamma.$$ Let $$C$$ be the point on $$\Gamma$$ apart from $$B$$ such that $$B'A= AC,$$ and let $$C'$$ be the diametrically opposite point of $$C$$ on $$\Gamma.$$ If $$AC'= 5,$$ find the distance between $$A$$ and $$B.$$
• The diametrically opposite point of $$X$$ on a circle $$\omega$$ is the unique point $$X'$$ on $$\omega$$ apart from $$X$$ such that $$XX'$$ is a diameter of $$\omega.$$