12.1 Tangent Lines
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Transcript of 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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Theorem 12.1
• If a line is tangent to a circle, then the line is perpendicular to the radius at the point of tangency.
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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°.
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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.
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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
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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
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Theorem 12.3
• If two tangent segments to a circle share a common endpoint outside the circle, then the two segments are congruent.
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More Practice!!!!!
• Homework – Textbook p. 767 # 6 – 17.