unusual centers
The center of a triangle can be outside the triangle
As crazy as it sounds, the circumcenter and orthocenter of a triangle can be
outside the triangle. This only happens if the triangle is obtuse (one angle
greater than 90º).
Circumc
enter
T
o draw the orthocenter
of an obtuse tr
iangle you
hav
e to ex
tend the sides.
Orthocenter
Right 90º
Equilateral 60º
Isoceles
ORTHOCENTER CIRCUMCENTER
On the 90º
vertex
On the
midpoint of the
hypotenuse
Exterior
Exterior
Interior on altitude
in line with other
centers
Interior on altitude
Same as all other
centers
Same as all other
centers
Triangle Centers Up Close
Obtuse
Acute
The centroid
and incenter
are always
interior.
Inside the tr
iangle
186 Chapter 4
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