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Theorem 12-1: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. Point of tangencyA B O P.

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Presentation on theme: "Theorem 12-1: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. Point of tangencyA B O P."— Presentation transcript:

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2 Theorem 12-1: If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. Point of tangencyA B O P AB  OP

3 Example: ML and MN are tangent to  O. Find the value of x. M L N O 117 0 x The sum of the angles of a quadrilateral is 360 0 117 0 +90 0 +90 0 +x=360 0 297 0 +x=360 0 x=63 0

4 Example: Is ML tangent to  N at L? M L 7 N 24 25 a 2 +b 2 =c 2 7 2 +24 2 =25 2 49+576=625 625=625 Yes

5 Theorem 12-1: The two segments tangent to a circle from a point outside of the circle are congruent. M L N O LM  NM

6 Example:  O is inscribed in  ABC. Find the perimeter of  ABC? C A 8 B 10 15 8 10 15 8+8+10+10+15+15 68

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