Question Video: Recognising Facts About Circle Construction Mathematics

True or False: A circle can be drawn through the vertices of any triangle.

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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.