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Lesson 6.1 – Properties of Tangent Lines to a Circle HW: Lesson 6.1/1-8

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If a line is tangent to a circle, then it is perpendicular to the radius drawn to the point of tangency. Radius to a Tangent Conjecture Using Properties of Tangents D

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Is TS tangent to R? Explain If the Pythagorean Theorem works then the triangle is a right triangle TS is tangent ? ? NO! ∆RST is not a right triangle so SR is not | to ST Using Properties of Tangents

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In the diagram, AB is a radius of A. Is BC tangent to A? Explain. Using Properties of Tangents If the Pythagorean Theorem works then the triangle is a right triangle BC is tangent ? ? NO! ∆ABC is not a right triangle so AB is not | to BC

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In the diagram, S is a point of tangency. Find the radius of r of circle T. Using Properties of Tangents 36+ r

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In the diagram, is a radius of P. Is P tangent to ? Using Properties of Tangents If the Pythagorean Theorem works then the triangle is a right triangle BC is tangent ? ? YES! ∆ABC is a right triangle so PT is | to TS

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If two segments from the same exterior point are tangent to the circle, then they are congruent. Tangent Segments Conjecture Using Properties of Tangents

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Tangent segments, from a common external point to their points of tangency, are congruent Using Properties of Tangents ● ●

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x 2 - 4 is tangent to R at S. is tangent to R at V. Find the value of x. Tangent segments are congruent Using Properties of Tangents

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Any two tangent lines of a circle are equal in length. 2x + 10 = 3x + 7 2x + 3 = 3x 3 = x Using Properties of Tangents

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In C, DA, is tangent at A and DB is tangent at B. Find x. Using Properties of Tangents ● ● 25= 6x -8 33= 6x 5.5 = x

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PRACTICE Using Properties of Tangents

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is tangent to C at S and is tangent to C at T. Find the value of x. is tangent to Q. Find the value of r. 28= 3x + 4 24= 3x 7 = x

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A tangent line is perpendicular to the radius of a circle, therefore use the Pythagorean Theorem to solve for the unknown length. a 2 = 6 2 + 8 2 a 2 = 36 + 64 a 2 = 100 a = 10 Using Properties of Tangents

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A tangent line is perpendicular to the radius of a circle, therefore use the Pythagorean Theorem to solve for the unknown length. Look for the length x, outside the circle. Let r be the radius of the circle, and let y = x + r. y 2 = 12 2 + 16 2 y 2 = 144 + 256 y 2 = 400 y = 20 x + 12 = 20 x = 20 - 12 x = 8 Since y = x + r and r = 12 y Using Properties of Tangents

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AB is tangent to C at B. AD is tangent to C at D. Find the value of x. x 2 + 2 11 = x 2 + 2 Two tangent segments from the same point are Substitute values AB = AD 9 = x 2 Subtract 2 from each side. 3 = x Find the square root of 9. Using Properties of Tangents

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Find the values of x, y, and z. All radii are ≅ y = 15 Tangent segments are ≅ z = 36 ∆UVR is a right triangle Using Properties of Tangents

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In the diagram, B is a point of tangency. Find the radius of C Using Properties of Tangents

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You are standing 14 feet from a water tower (R). The distance from you to a point of tangency (S) on the tower is 28 feet. What is the radius of the water tower? Radius = 21 feet Tower ● Using Properties of Tangents

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Is tangent to C ?

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Find the value of x. Using Properties of Tangents

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