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Name: Date: Geometry 10.1-10.3 Quiz Review 10.1 Tangents to Circles 1. chord 2. secant 3. radius 5. tangent 6. radius 7. chord What is a tangent line? 4. diameter 8. radius A line that touches the circle at exactly one point. How can you tell if a common tangent is internal or external? Internal: cuts through the segment connecting the two centers of the circles. External: doesn’t. 9. Draw in a common internal tangent and a common external tangent. Label which is which. external internal 10. Tell whether line AB is tangent to circle C. Explain your reasoning. Yes; 72 + 242 = 252, so by Pythagorean Thm. Converse, ΔABC is a right triangle and the radius CA is perpendicular to BA. So BA must be a tangent. 11. Lines AB and AD are tangent to circle C. Find the value of x. Explain your reasoning. Tangent segments (BA and DA) from the same exterior point (A) are congruent, so 2x + 8 = 4x. x = 4. Name: Date: Geometry 10.2 Arcs and Chords 1. a) 110º b) 200º c) 160º d) 250º 2. Use the given information to find the value of x. Explain which theorems you needed to use. x Since chords AB and DE are both 10, they are equidistant from the center. So CF = CG = x. Since CG is perpendicular to DE and is a diameter (if you extend it), it must also bisect DE. So DE = GE = 5. Then by the Pythagorean theorem, x2 + 52 = 62, so x = √11. 10.3 Inscribed Angles Explain how to find the center of a circle using two chords. Draw two chords. Find the perpendicular bisector of each chord. Each must be a diameter. Their intersection must be the center. How do you find the measure of an inscribed angle? Measure of inscribed angle = ½ measure of intercepted arc OR measure of intercepted arc = 2*measure of inscribed angle What do you know about an inscribed triangle? an inscribed quadrilateral? If one side of the triangle is a diameter, then the angle opposite it is a right angle (i.e., that diameter is the hypotenuse). A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary. Find the value of each variable. 1. 3. Inscribed angle = ½ intercepted arc These angles are inscribed angles sharing the same intercepted arc, so they are congruent. 3x = ½ 138 80 = 3x + 5 3x = 69 75 = 3x x = 23 25 = x 2. 4. Inscribed quad. has opposite angles supplementary. Since the inscribed angle is right, the segment is a diameter. So the arc is a semicircle. 2x + x + 12 = 180º 4x + 8 = 180º 3x = 168 4x = 172 x = 56 x = 43 4y + 5y = 180º 9y = 180 y = 20