Video Transcript
True or false: a circle can be
drawn through the vertices of any triangle.
To answer this question, we might
start by drawing a triangle and seeing how we might construct a circle which passes
through all three vertices of the triangle. However, this is not necessary
since we can just recall a useful fact about circles. We know that any three noncolinear
points have a unique circle which passes through all three points, where we remember
noncolinear points means they don’t lie on the same straight line. And the vertices of a triangle
don’t lie on the same straight line. That’s what it means for a shape to
be a triangle. For example, if we had three points
which lied on a straight line and we tried to connect the vertices together, we
would just end up with a straight line.
Therefore, we can just apply this
property to show that the answer is true. A circle can be drawn through the
vertices of any triangle. This is called the circumcircle of
the triangle.
