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GEOMETRY: Chapter 10 10.4: Other Relationships in Circles Theorem 10.12 If a tangent and a chord intersect at a point on a circle, then the measure of each angle formed is one half the measure of its intercepted arc. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 680. Ex.1: Line m is tangent to the circle. Find x or y. Answer: a. 114; b. 236 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681. Intersecting Lines and Circles If two lines intersect a circle, there are three places where the lines can intersect. Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681. Angles Inside the Circle Theorem If two chords intersect inside a circle, then the measure of each angle is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle. Theorem 10.13: Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681. Angles Outside the Circle Theorem If a tangent and a secant, two tangents, or two secants intersect outside a circle, then the measure of the angle formed is one half the difference of the measures of the intercepted arcs. Theorem 10.14 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681. Ex. 2: Find the value of x. Answer: 76 Image taken from: Geometry. McDougal Littell: Boston, 2007. P. 681. Ex. 3: Find the value of x. Answer: 18 Images taken from: Geometry. McDougal Littell: Boston, 2007. P.682. Ex. 4: The Space Shuttle typically orbits at a height of 600 kilometers. Suppose an astronaut takes a picture from point S. What is the measure of arc RQ? Answer: 48o Images taken from: Geometry. McDougal Littell: Boston, 2007. P.682. 10.4, p. 624, #5-28 all