Calculate the length of AC

Question

The diameter $AB$ of the circle is $10\,\text{cm}$. The length of $BC$ is $6\,\text{cm}$. Calculate the length of $AC$.

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I'm doing a mock exam and I'm not sure how to work out the length of $AC$. Any ideas? Thanks.

Answer 1

The Pythagorean Theorem applies: the right angle is $\angle ACB$, by Thales Theorem. So the hypotenuse is $AB = 10$.

$$\begin{align} |AB|^2 & = |AC|^2 + |BC|^2 \\ \\ \iff |AC|^2 & = |AB|^2 - |BC|^2 \\ \\ \iff |AC| & = \sqrt{10^2 - 6^2} = \sqrt{64} = 8\end{align}$$