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# Sphere

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Points A, B, and C are on a sphere whose radius is 13.  If AB = BC = $$12$$ , what is the longest possible value of AC?

Apr 25, 2022

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What is the longest possible value of AC?

Hello Guest!

$$\sqrt{12^2-x^2}+\sqrt{13^2-x^2}=13\\ x=\dfrac{12\sqrt{133}}{13}$$

$$The\ longest\ possible\ value\ of\ AC\ is\ {\color{blue}2x}=2\cdot \dfrac{12\sqrt{133}}{13}=\color{blue}21.291$$

!

Apr 26, 2022