Problem 23 of 34geo-023
A circle with center has a radius of 8 centimeters. Point lies outside the circle, and a line through is tangent to the circle at point . If centimeters, what is the distance, in centimeters, from to the point on the circle that is closest to ?
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Solution walkthrough1:38
- A radius drawn to the point where a tangent touches the circle is perpendicular to the tangent: angle .
- Join to . Triangle is a right triangle with legs and , and hypotenuse .
- , so .
- The closest point is where segment crosses the circle. is a radius, so .
- Traps: is , the distance to the center. treats as the hypotenuse. adds the legs.