15.3 Tangents and Circumscribed Angles

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Presentation transcript:

15.3 Tangents and Circumscribed Angles What are the key theorems about tangents to a circle?

Tangent- a line in the same plane as a circle that intersects the circle in exactly one point Point of tangency- the point where a tangent and a circle intersect The line is tangent to circle C and point P is the point of tangency.

Tangent-Radius Theorem: If a line is tangent to a circle, then it is perpendicular to a radius drawn to the point of tangency

Example: Is EF tangent to Circle D? 61 11 F E 60

Circumscribed Angle- an angle formed by 2 rays from a common endpoint that are tangent to a circle

A B D C m<ABC + m<ADC = 180°

XA and XB are tangent lines to Circle C. Find m<X. (2y)° (4y)°

Tear out Pages 800-803 and circle the following problems: 5, 6, 10, 11, 13, 19 Tear out Page 810-811 and circle 8, 9, 12, 13, 14

p. 800-803 5. 95° 6. 212° <P= 90, <Q=140 <R=90, <S=40 11. <D=65, <A=70 <B= 115, <C=110 13. <W=94, <V= 101 <T=79, <U=86 <J= 108° <K= 81° <L= 72° <M= 99° p. 810-811 8. 13 9. 32(set sides equal to each other and you will need to use the quadratic formula) 12. 138° 13. 45° 14. 124°