12.1 Tangent Lines
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12.1 Tangent Lines •A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. • The point where a circle and a tangent intersect is the point of tangency.
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12.1 Tangent Lines. A tangent to a circle is a line in the plane of the circle that intersects the circle in exactly one point. The point where a circle and a tangent intersect is the point of tangency. Theorem 12.1. - PowerPoint PPT Presentation
Transcript of 12.1 Tangent Lines
12.1 Tangent Lines• A tangent to a circle is a line in the plane of the
circle that intersects the circle in exactly one point.• The point where a circle and a tangent intersect is the
point of tangency.
Theorem 12.1
• If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency.
Finding Angle Measures• Segment ML and segment MN are tangent to circle O.
What is the value of x?
LMNO is a quadrilateral.
The sum of the angles is 360.
90 + 117 + 90 + x = 360
297 + x = 360
x = 63
The measure of angle M is 63°.
Theorem 12.2
• If a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle.
Finding a Radius• What is the radius of circle C?
2 2 2AB BC AC 2 2 212 ( 8)x x
2 2144 16 64x x x 16 80x
5x
Identifying a Tangent• Is segment ML tangent to circle N at L? Explain.
2 2 2NL ML NM ?
2 2 27 24 25 625 625
Theorem 12.3
• If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.
More Practice!!!!!
• Homework – Textbook p. 767 # 6 – 17.
