Tangents and Circles
More Lessons for High School Regents Exam
Math Worksheets
High School Math based on the topics required for the Regents Exam conducted by NYSED.
Theorems for Circles and Tangents:
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. 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.
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.
Solving some problems using properties of tangents to a circle
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