In geometry, a tangent to a circle is a straight line that touches the circle at only one point, called the point of tangency. The tangent is always perpendicular to the radius drawn to the point of tangency. Understanding this relationship is crucial for solving many circle-related problems. This worksheet will help you explore properties of tangents and practice applying them.
Match the term with its definition:
| Term | Definition |
|---|---|
| 1. Tangent | A. The distance from the center of the circle to any point on the circle. |
| 2. Radius | B. A line segment connecting two points on a circle. |
| 3. Chord | C. The point where a tangent line touches the circle. |
| 4. Point of Tangency | D. A line that touches a circle at only one point. |
| 5. Secant | E. A line that intersects a circle at two points. |
Complete the following paragraph with the correct words:
A __________ is a line that touches a circle at only one __________. The __________ is always perpendicular to the __________ drawn to the point of tangency. If two tangents are drawn from the same external __________, they are __________ in length.
Explain, in your own words, why a tangent line is always perpendicular to the radius at the point of tangency. Use a diagram to support your explanation.
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