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Published byLawrence Brookings Modified over 2 years ago

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OBJECTIVES: STUDENTS WILL BE ABLE TO… USE THE RELATIONSHIP BETWEEN A RADIUS AND A TANGENT USE THE RELATIONSHIP BETWEEN 2 TANGENTS FROM ONE POINT FIND THE MEASURE OF AN ANGLE FORMED BY 2 TANGENTS INTERSECTING OUTSIDE THE CIRCLE 11.1: Tangent lines

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Warm Up K B C A 85° 1.Name a minor arc and find its measure. 2.Find measure of

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DEFINITION TANGENT TO A CIRCLE: Line in the plane of the circle that intersects the circle at exactly one point. POINT OF TANGENCY: Where the circle and the tangent line intersect

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THEOREM If a line is tangent to a circle, then the line is perpendicular to the radius drawn to the point of tangency.

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Find the value of x. Assume the lines are tangent to the circle. x°110°

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Find x. Assume the line is tangent. B A C 42° x°

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Find x. Assume AB is tangent to the circle. B A x° 60° C

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Theorem 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. Line AB is tangent to circle O.

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Is segment AB tangent to the circle? 24 7 27 B A

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Is segment AB tangent to the circle? 15 5 16 A B

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DEFINITIONS A polygon is inscribed in a circle if all vertices of the polygon lie on the circle. A polygon is circumscribed about the circle if each side of the polygon is tangent to the circle.

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THEOREM The 2 segments tangent to a circle from a point outside the circle are congruent.

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EXAMPLE: Find x. The lines are tangent to the circle. 17 x

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Find x 2x+7 21

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Find the perimeter.

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You try….find the perimeter.

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Theorem: The measure of an angle formed by 2 lines that intersect outside a circle is half the difference of the measures of the intercepted arcs. In other words, the measure of angle 1 is…

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Example: Find x.

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6.5Apply Other Angle Relationships Theorem 6.13 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one.

6.5Apply Other Angle Relationships Theorem 6.13 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one.

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