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A point $P$ is 17 cm away from the center of a circle. A tangent is drawn from $P$ to the circle, and its length is 15 cm. What is the area of the circle?

1. 64 $\pi$ cm²
2. 289 $\pi$ cm²
3. 225 $\pi$ cm²
4. 81 $\pi$ cm²

Correct answer: 64 $\pi$ cm²

Solution

The radius to the point of tangency is perpendicular to the tangent, so the center, point of tangency, and external point form a right triangle. Using Pythagoras, $r^2+15^2=17^2$, so $r^2=289-225=64$. Hence the area is $\pi r^2=64\pi$ cm².

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