Question

circle a has a diameter of 10 units. (overrightarrow{bc}) is tangent to circle a, and bc has a length of 12 units. what is the length of (overline{ac})? units

Explanation:

Step1: Find the radius of circle A

Since the diameter of circle A is 10 units, the radius \(AB=\frac{10}{2} = 5\) units.

Step2: Use the Pythagorean theorem

Because \(BC\) is tangent to circle A at point B, \(\angle ABC = 90^{\circ}\). In right - triangle \(ABC\), by the Pythagorean theorem \(AC^{2}=AB^{2}+BC^{2}\). We know \(AB = 5\) units and \(BC=12\) units. Then \(AC^{2}=5^{2}+12^{2}=25 + 144=169\).

Step3: Solve for \(AC\)

Take the square root of both sides: \(AC=\sqrt{169}=13\) units.

Answer:

13