Circles, IV

Circles, IVTangentsDefinition - TangentsRay BC is tangent to circle A, because the line containing BC intersects the circle in exactly one point. This point is called the point of tangency.

TheoremIf a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency.

Example 1 Tangent Lines

Example 1 Tangent Lines

Example 1 Tangent Lines

Example 1 Tangent Lines

Example 1 Tangent Lines

Example 1 Tangent Lines

Example 2 Tangent Lines

Example 2 Tangent Lines

Example 2 Tangent Lines

Example 2 Tangent Lines

Example 2 Tangent Lines

Example 2 Tangent Lines

Example 2 Tangent Lines

Example 2 Tangent Lines

Theorem The converse is also trueIf a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.

Example 3 Showing Tangency

Example 3 Showing Tangency

Example 3 Showing Tangency

Example 3 Showing Tangency

Example 3 Showing Tangency

Example 3 Showing Tangency

Example 3 Showing Tangency

Example 4 Non Tangent Segment

Example 4 Non Tangent Segment

Example 4 Non Tangent Segment

Example 4 Non Tangent Segment

Example 4 Non Tangent Segment

Example 4 Non Tangent Segment

Example 4 Non Tangent Segment

Example 4 Non Tangent Segment

Example 4 Non Tangent Segment

Example 4 Non Tangent Segment

Example 4 Non Tangent Segment

Example 5Determine if the segments are tangent to the respective circles

CWTangent Lines of CirclesTheoremIf two segments from the same exterior point are tangent to a circle, then they are congruent.

Example 1

Example 1

Example 1

Example 1

Example 1

Example 1

Example 1

Example 1

Example 1

Example 1

Example 2 Circumscribed Triangles & Perimeter