Pre-Calc Exam Notes 61

Pre-Calc Exam Notes 61 - Circumscribed and Inscribed...

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Circumscribed and Inscribed Circles Section 2.5 61 For the right triangle in the above example, the circumscribed circle is simple to draw; its center can be found by measuring a distance of 2.5 units from A along AB . We need a different procedure for acute and obtuse triangles, since for an acute triangle the center of the circumscribed circle will be inside the triangle, and it will be outside for an obtuse triangle. Notice from the proof of Theorem 2.5 that the center O was on the perpendicular bisector of one of the sides ( AB ). Similar arguments for the other sides would show that O is on the perpendicular bisectors for those sides: Corollary 2.7. For any triangle, the center of its circumscribed circle is the intersection of the perpendicular bisectors of the sides. A B d d Figure 2.5.4 Recall from geometry how to create the perpendicular bisector of a line segment: at each endpoint use a compass to draw an arc with the same radius. Pick the radius large enough so that the arcs intersect at two points, as in Figure 2.5.4. The line through
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