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Tangents and Circles

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Examples, videos, worksheets, solutions, and activities to help Geometry students learn about the tangents of a circle.

What is a tangent?
A tangent is a line in the plane of a circle that intersects the circle at one point.

What is a common tangent?
A common tangent is a line that is a tangent to each of two coplanar circles.

What is a common external tangent?
A common external tangent does not intersect the segment that joins the centers of the circles.

What is a common internal tangent?
A common internal tangent intersects the segment that joins the centers of the circles.

The following diagrams show some examples of common external tangents and common internal tangents. Scroll down the page for more examples and solutions of common external tangents and common internal tangents.

Common Tangents

Tangent Line - Geometry Help
Students learn the definitions of a tangent. Common Internal and External Tangents
Students learn the definitions of common internal tangents and common external tangents.

Tangents and Circles
Students learn the following theorems related to tangents. If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency. If a line is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle. Radii to Tangents
When a radius is drawn to a point of tangency, the angle formed is always a right (90 degree) angle. This fact is commonly applied in problems with two tangent segments drawn to a circle from a point. If two radii to tangents are drawn in, a kite with two right angles is formed and the missing angles or sides can be found. Related topics include central angles, tangent segments to a circle, and chords. Tangent Segments to a Circle
A tangent intersects a circle in exactly one point. When two segments are drawn tangent to a circle from the same point outside the circle, the segments are congruent. The extension problem of this topic is a belt and gear problem which asks for the length of belt required to fit around two gears. 3 problems including common internal tangent and common external tangent
1. Calculate a radius given a tangent segment length.
2. Calculate the length of a common external tangent segment.
3. Calculate a radius, given the length of a common internal tangent segment.

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