Constructing Circumscribed Circles Adapted from Walch
Education
Slide 3
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
Slide 4
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
Slide 5
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
Slide 6
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
Slide 7
Construct the perpendicular bisector of 3.2.2: Constructing
Circumscribed Circles6
Slide 8
Repeat the process for and 3.2.2: Constructing Circumscribed
Circles7
Slide 9
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
Slide 10
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
Slide 11
See if you can O Construct a circle circumscribed about acute
3.2.2: Constructing Circumscribed Circles10