True or false? A radius meets a tangent line at a 90° angle.
Answer (2)
A radius and a tangent line are geometric concepts related to circles.
The tangent-radius theorem states that a tangent line to a circle is perpendicular to the radius at the point of tangency.
This means the angle between the radius and tangent line is always 90 degrees.
Therefore, the statement is T r u e .
Explanation
Problem Analysis Let's analyze the problem. We need to determine if the statement "A radius meets a tangent line at a 90° angle" is true or false. This is a fundamental concept in geometry related to circles and tangent lines.
Recall the Tangent-Radius Theorem Recall the theorem regarding the relationship between a radius and a tangent line at the point of tangency. The theorem states: A tangent line to a circle is perpendicular to the radius drawn to the point of tangency. This means that the angle between the radius and the tangent line at their point of intersection is always 90 degrees.
Conclusion Based on the theorem, the statement "A radius meets a tangent line at a 90° angle" is true.
Examples
Imagine you're designing a circular garden and want to build a straight fence (tangent line) along one edge. To ensure the fence is perfectly aligned with the garden's edge, you would draw a line from the center of the garden (radius) to the point where the fence touches the garden's edge. The tangent-radius theorem guarantees that this radius will always meet the fence at a 90-degree angle, ensuring a precise and stable construction.
The statement "A radius meets a tangent line at a 90° angle" is true based on the tangent-radius theorem. This theorem states that a tangent line is always perpendicular to the radius drawn to the point of tangency. Therefore, at the point where they meet, they form a right angle of 90 degrees.
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