 # Tangents and Circles

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More Lessons for Grade 9

Math Worksheets

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.

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.

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