Triangle: Circumcenter
How to use the property of the circumcenter of a triangle: definition, property, 1 example, and its solution.
Definition
The circumcenter of a triangle
is the center of the circle
that circumscribes the inner triangle.
Property
Three perpendicular bisectors of the sides
meet at the circumcenter.
Example
Solution
Solution (Detail)
It says
point O is the circumcenter.
So, to remind yourself that
point O is the circumcenter,
lightly draw the circumscribed circle.
OM is perpendicular to BC.
Then OM is the perpendicular bisector of BC.
So BM = MC.
See △OBM.
It's a right triangle.
The sides are (3, BM, 5).
So △OBM is a (3, 4, 5) right triangle.
Pythagorean Triple
So BM = 4.
BM = MC
BM = 4
So MC = 4.
BM = 4
MC = 4
So BC = 4 + 4.
4 + 4 = 8
So BC = 8.