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Constructing Circumscribed Circles Adapted from Walch Education

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Key Concepts The perpendicular bisector of a segment is a line that intersects a segment at its midpoint at a right angle. When all three perpendicular bisectors of a triangle are constructed, the rays intersect at one point. This point of concurrency is called the circumcenter. 3.2.2: Constructing Circumscribed Circles2

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Key Concepts, continued The circumcenter is equidistant from the three vertices of the triangle and is also the center of the circle that contains the three vertices of the triangle. A circle that contains all the vertices of a polygon is referred to as the circumscribed circle. 3.2.2: Constructing Circumscribed Circles3

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Key Concepts, continued When the circumscribed circle is constructed, the triangle is referred to as an inscribed triangle, a triangle whose vertices are tangent to a circle. 3.2.2: Constructing Circumscribed Circles4

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Practice Verify that the perpendicular bisectors of acute are concurrent and that this concurrent point is equidistant from each vertex. 3.2.2: Constructing Circumscribed Circles5

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Construct the perpendicular bisector of 3.2.2: Constructing Circumscribed Circles6

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Repeat the process for and 3.2.2: Constructing Circumscribed Circles7

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Locate the point of concurrency. Label this point D O The point of concurrency is where all three perpendicular bisectors meet. 3.2.2: Constructing Circumscribed Circles8

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Verify that the point of concurrency is equidistant from each vertex. O Use your compass and carefully measure the length from point D to each vertex. The measurements are the same. 3.2.2: Constructing Circumscribed Circles9

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See if you can O Construct a circle circumscribed about acute 3.2.2: Constructing Circumscribed Circles10

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Thanks for Watching!!! ~ms. dambreville