n roblem 1 Finding ngle Measures Multiple hoice ML and MN are tangent to }. So the assumption that n is not perpendicular to must be false. For two points on n to also be on } contradicts the given fact that n is tangent to } at. So K and are both on } n L K by the definition of a circle. Since corresponding parts of congruent triangles are congruent, K. LK L because perpendicular lines form congruent adjacent angles. lso there is a point K on n such that LK L. If line n is not perpendicular to, then, for some other point L on n, L must be perpendicular to n. rove: Step 1 Step 2 Step 3 n # ssume that n is not perpendicular to. # 762 hapter 12 irclesĢ roof Indirect roof of Theorem 12-1 Given: n is tangent to } at. Theorem 12-1 Theorem 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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ssential Understanding radius of a circle and the tangent that intersects the endpoint of the radius on the circle have a special relationship. is a tangent ray and is a tangent segment. The point where a circle and a tangent intersect is the point of tangency. tangent to a circle is a line in the plane of the circle that intersects the circle in eactly one point. This use of the word tangent is related to, but different from, the tangent ratio in right triangles that you studied in hapter 8.
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Lesson L VocabularyV tangent to a circle point of tangency In the Solve It, you drew lines that touch a circle at only one point. Make a conjecture about the lengths of the two segments formed when the rays touch the circle. onsider any two rays with a common endpoint outside the circle. Repeat the procedure with a point farther away from the circle. ach ray from oint touches the circle in only one place no matter how far it etends. MTHMTIL RTIS raw a diagram like the one at the right. M 1, M 3, M 4 bjective To use properties of a tangent to a circle Try this again with a different circle. the radius of a circle is perpendicular to the tangent where the radius intersects the circle.
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1 12-1 Tangent Lines ommon ore State Standards G-.2 Identify and describe relationships among inscribed angles, radii, and chords.