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Name Class Date 1 2_1 Reteaching Tangent Lines A tangent is a line that touches a circle at exactly one point. In the diagram, E is tangent to 69. You can apply theorems about tangents to solve problems. Theorem 12-1 If a line is tangent to a circle, then that line forms a right angle with the radius at the point where the line touches the circle. Theorem 12-2 If a line in the same plane as a circle is perpendicular to a radius at its endpoint on the circle, then the line is tangent to the circle. Problem Use the diagram at the right to solve the problems below. (5 is tangent to GE What is the measure of AG? What is the length of the radius? 35331-153 GH i5 tangent to 0-K: it You can use the Pythagorean forms a right angle with the radius. _ _ Theorem to nd nnssmg lengths. The sum of the angles of a triangle is always 180. Write an equation to W +H02 = 0K2 nd mlG. r2+122=(9+r)2 mZG+mH+mAK=180 r2+144=(9+r)(9+r) mZG+90+68=180 r2+144=81+18r+r2 sz+158=180 63=18r sz=22 3.5 =r So, the measure ofAG is 22 and the length ofthe radius is 3.5 units. Exercises In each circle, what is the value of x? 2. I 3. I Sawas Texas Geometry Copyright Q by Weamlng Company LLC. All Rights Reserved. Name Class Date 12-1 Reteaching (continued) Tangent Lines In each circle, what is the value of r? 5. 15 6. 8/ 14 O. Theorem 12-3 If two segments are tangent to a circle from the same point A B outside the circle, then the two segments are equal in length. D . In the diagram, AB and BC are both tangent to OD. So, they are also congruent. When circles are drawn inside a polygon so that the sides of the polygon are tangents, the circle is inscribed in the 9 in figure. You can apply Theorem 12-3 to find the perimeter, or distance around the polygon. 5 in D Problem 3 in. OM is inscribed in quadrilateral ABCD. What is the perimeter of ABCD? 2 in. ZA = AW = 9 WB = BX = 5 CY = XC = 2 YD = DZ = 3 Now add to find the length of each side: AB = AW + WB = 9 +5 =14 BC = BX + CX = 5+2=7 CD = CY + YD = 2+3 =5 DA = DZ + ZA = 3 + 9 =12 14 +7+5+12=38 The perimeter is 38 in. Exercises Each polygon circumscribes a circle. What is the perimeter of each polygon? 7 8. 9. 7.5 ft 4 ft 3.5 cm 3 cm 8 cm 6 ft 5.25 cm 8.75 cm Savvas Texas Geometry Copyright @ by Sexwas Learning Company LLC. All Rights Reserved