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Find the area of the triangle enclosed by the common tangents to the circles x² + y² - 6x = 0 and x² + y² + 2x = 0.
- 3√3
- 2√3
- 9√3
- 6√3
Correct answer: 3√3
Solution
The area of the triangle formed by the common tangents to the two circles can be calculated using the formula for the area of a triangle given the lengths of the tangents. The specific configuration of the circles leads to an area of 3√3, which is derived from the geometric properties of the tangents and the distance between the centers of the circles.
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