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FeatureLesson Geometry Lesson Main PA and PB are tangent to C. Use the figure for Exercises 1–3. 1.Find the value of x. 2.Find the perimeter of quadrilateral PACB. 3.Find CP. HJ is tangent to A and to B. Use the figure for Exercises 4 and 5. 4.Find AB to the nearest tenth. 5.What type of special quadrilateral is AHJB? Explain how you know cm 29 cm 20.4 cm Lesson 12-1 Tangent Lines... Trapezoid; the tangent line forms right angles at vertices H and J, so HA || JB. Because HA = JB, AHJB is not a parallelogram but a trapezoid. / Lesson Quiz 12-2

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FeatureLesson Geometry Lesson Main (For help, go to Lesson 8-2.) Lesson 12-2 Find the value of each variable. Leave your answer in simplest radical form Chords and Arcs Check Skills Youll Need 12-2

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FeatureLesson Geometry Lesson Main Lesson 12-2 Chords and Arcs Notes 12-2 A segment whose endpoints are on a circle is called a chord.

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FeatureLesson Geometry Lesson Main Lesson 12-2 Chords and Arcs Notes 12-2

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FeatureLesson Geometry Lesson Main Lesson 12-2 Chords and Arcs Notes 12-2

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FeatureLesson Geometry Lesson Main Lesson 12-2 Chords and Arcs Notes 12-2

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FeatureLesson Geometry Lesson Main Lesson 12-2 Chords and Arcs Notes 12-2

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FeatureLesson Geometry Lesson Main Lesson 12-2 Chords and Arcs Notes 12-2

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FeatureLesson Geometry Lesson Main Lesson 12-2 Chords and Arcs Notes 12-2

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FeatureLesson Geometry Lesson Main Lesson 12-2 Chords and Arcs Notes 12-2

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FeatureLesson Geometry Lesson Main AOX BOX by the definition of an angle bisector. Lesson 12-2 Chords and Arcs In the diagram, radius OX bisects AOB. What can you conclude? AX BX because congruent central angles have congruent chords. AX BX because congruent chords have congruent arcs. Quick Check Additional Examples 12-2 Using Theorem 12-4

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FeatureLesson Geometry Lesson Main QS = QR + RSSegment Addition Postulate QS = 7 + 7Substitute. QS = 14Simplify. AB = QSChords that are equidistant from the center of a circle are congruent. AB = 14Substitute 14 for QS. Find AB. Lesson 12-2 Chords and Arcs Quick Check Additional Examples 12-2 Using Theorem 12-5

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FeatureLesson Geometry Lesson Main OP 2 = PM 2 + OM 2 Use the Pythagorean Theorem. r 2 = Substitute. r 2 = 289Simplify. r = 17Find the square root of each side. PM = PQA diameter that is perpendicular to a chord bisects the chord PM = (16) = 8Substitute The radius of O is 17 in.. Draw a diagram to represent the situation. The distance from the center of O to PQ is measured along a perpendicular line.. P and Q are points on O. The distance from O to PQ is 15 in., and PQ = 16 in. Find the radius of O... Lesson 12-2 Chords and Arcs Quick Check Additional Examples 12-2 Using Diameters and Chords

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FeatureLesson Geometry Lesson Main

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FeatureLesson Geometry Lesson Main For Exercises 1–5, use the diagram of L. 1.If YM and ZN are congruent chords, what can you conclude? 2.If YM and ZN are congruent chords, explain why you cannot conclude that LV = LC. 3.Suppose that YM has length 12 in., and its distance from point L is 5 in. Find the radius of L to the nearest tenth. For Exercises 4 and 5, suppose that LV YM, YV = 11 cm, and L has a diameter of 26 cm. 4.Find YM. 5.Find LV to the nearest tenth.... YM ZN; YLM ZLN 6.9 cm 22 cm 7.8 in. Lesson 12-2 Chords and Arcs You do not know whether LV and LC are perpendicular to the chords. Lesson Quiz 12-2

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FeatureLesson Geometry Lesson Main Lesson 12-2 Chords and Arcs Solutions Check Skills Youll Need 1.The triangle is a 45°-45°-90° triangle, so each leg is the length of the hypotenuse divided by 2 : = =, or The triangle is a 45°-45°-90° triangle, so each leg is the length of the hypotenuse divided by 2: = 5 3.The triangle is a 30°-60°-90° triangle, so the hypotenuse is twice the length of the side opposite the 30° angle: 2(14) =

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