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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 Fall '11
 Dr.Cheun
 Calculus, Geometry, Pythagorean Theorem, triangle, Perpendicular Bisectors

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