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1. 5. 4. 3. 2.

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Tangents Sec: 12.1 Sol: G.11a,b

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A line is ______________________ to a circle if it intersects the circle in exactly one point. This point is called the point of _______________________________.

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Consider the following diagram:

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Example: If RT is tangent to Circle O, Then OR RT

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The converse of the last theorem is also true. This means: In a plane, if a line is perpendicular to a radius of a circle at the endpoint on the circle, then the line is a tangent of the circle. If OR RT, RT is tangent to Circle O

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If a line is tangent to a circle, then it is ________________________________ to the radius drawn to the point of tangency. Example:

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Example:

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Theorem 10.11: If two __________from the same exterior point are tangent to a circle, then the two segments are ______. Example: AB CB

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117° X°

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Example x+4 y 10 y-5

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Circumscribed polygons: A polygon is circumscribed about a circle if each side of the polygon is tangent to the circle. ◦ Example:

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Example: Triangle HJK is circumscribed about circle G. Find the Perimeter of HJK if NK = JL+29. 45 18 JL + 29

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Arcs and Chords Sec: 12.2 Sol: G.11a,b

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Recall the definitions of minor arcs & chords (draw an example of each on A below): Example: When minor arc and a chord share the same endpoints, we call the arc the arc of the chord. Example:

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In a circle or in congruent circles, two __________ ________ are congruent if and only if their corresponding chords are congruent. Example: In A, if, then ____ ____.

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In a circle, if a diameter is perpendicular to a chord, then it bisects the chord and its arc. Example:

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In a circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center. Example:

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Find x in each problem. 1. 2. Suppose a chord of a circle is 10 inches long and is 12 inches from the center of the circle. Find the length of the diameter. 3. Suppose the diameter of a circle is 34 inches long and a chord is 30 inches long. Find the distance between the chord and the center of the circle. 4. Suppose a chord of a circle is 24 cm long and is 15 cm from the center of the circle. Find the length of the radius.

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Suggested Assignments Classwork: Handouts Homework: Pg 767 6-8,12-18even,19,26 and Pg 776 6-10Even, 13-16,30

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10-5 Tangents You used the Pythagorean Theorem to find side lengths of right triangles. Use properties of tangents. Solve problems involving circumscribed.

10-5 Tangents You used the Pythagorean Theorem to find side lengths of right triangles. Use properties of tangents. Solve problems involving circumscribed.

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