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Tangents and Circles

High School Math based on the topics required for the Regents Exam conducted by NYSED.

Theorems:
1) If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency.

2) Tangent segments to a circle from the same external point are congruent.

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. Topics related to circle radii include inscribed circles and radii to tangents.

Tangents to a Circle
In this lesson we looked at properties of tangents to a circle If a line is tangent to a circle, it is perpendicular to the radius drawn to the point of tangency. Tangent segments to a circle from the same external point are congruent.

Tangents and Circles
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.

Tangents to a Circle
Solving some problems using properties of tangents to a circle

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