11.1.1 Lines That Intersect Circles (continued)
Example 2 Identifying Tangents of Circles
Attributes of two circles are identified in this example. The circles are drawn in the coordinate plane. The length of the radius of circle A can be determined by counting along the x -axis, since the center of circle A is on the x -axis at A (2, 0). The length of the radius of circle A is 6 units. The length of the radius of circle B can also be determined by counting along the x -axis, since it is centered at B (4, 0). The length of the radius of circle B is 3 units. The point of tangency of the line intersecting with circle A appears to be (1, − 6). The equation of the tangent line to circle A is y = − 6.
Example 3 Problem-Solving Application
A line tangent to a circle is perpendicular to the radius that extends from the center of the circle to the point of tangency. A line that is perpendicular to a radius of a circle at a point on the circle is tangent to the circle.
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