A tangent line is a line that touches a circle or curve at only one point, called the point of tangency. Understanding the properties of tangent lines is crucial in geometry because they relate to radii, angles, and other geometric figures. A key property is that a tangent line is always perpendicular to the radius drawn to the point of tangency. This allows us to use the Pythagorean theorem and trigonometric ratios to solve many problems involving tangents.
Tangent lines also have interesting relationships with segments drawn from external points to a circle. If two tangent segments are drawn to a circle from the same external point, then those segments are congruent. Knowing these properties helps in calculating lengths, angles, and proving congruency in geometric figures. Let's practice with some exercises!
Match each term with its correct definition:
| Term | Definition |
|---|---|
| 1. Tangent Line | A. The point where a tangent line touches a circle. |
| 2. Point of Tangency | B. A line that intersects a circle at exactly one point. |
| 3. Radius | C. A line segment from the center of a circle to any point on the circle. |
| 4. Secant | D. A line that intersects a circle at two points. |
| 5. Congruent Segments | E. Line segments that have the same length. |
Complete the following paragraph using the words provided: perpendicular, congruent, external, radius, point of tangency.
A tangent line to a circle is always ________ to the ________ at the ________. If two tangent segments are drawn to a circle from the same ________ point, then those segments are ________.
Explain why a line that intersects a circle at two points cannot be a tangent line. Use geometric principles to support your explanation.
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