Tangent/Radius Theorems

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Presentation transcript:

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

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.

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. A P B O

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

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. A P B O

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

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

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

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

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