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11-1 Tangent Lines  Tangent/Radius Theorems  Two Tangents Theorem.

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Presentation on theme: "11-1 Tangent Lines  Tangent/Radius Theorems  Two Tangents Theorem."— Presentation transcript:

1 11-1 Tangent Lines  Tangent/Radius Theorems  Two Tangents Theorem

2 Vocabulary  Tangent to a circle  Point of tangency  A line in the same plane of a circle that intersects the circle in exactly one point.  The point where a circle and a tangent intersect.

3 Theorem 11-1 If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency. P O A B

4 #1 Finding Angle Measures is tangent to. Find the value of x. D O xoxo E 38 o

5 Theorem 11-2 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. P O A B

6 #2 Finding a Tangent A belt fits tightly around two circular pulleys. Find the distance between the centers of the pulleys. P O 4 cm 3 cm 15 cm x 7 cm 3 cm 15 cm

7 #3 Finding a Tangent If NL = 4, LM = 7, and NM = 8, is tangent to a at L? N L M 4 7 8

8 Vocabulary  Inscribed in  Circumscribed about  All vertices of a figure lie on the circle.  When a circle is inscribed in a figure.

9 Theorem 11-3 The two segments tangent to a circle from a point outside the circle are congruent. A O B C

10 #4 Circles Inscribed in Polygons Circle O is inscribed in Triangle PQR. Triangle PQR has a perimeter of 88 cm. Find QY. P O Q R X Z Y 17 cm 15 cm 17 cm x x


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