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What is a nine point circle? In geometry the nine point circle is a circle that can be constructed for any given triangle. It is named a nine point circle because it passes through nine significant points that are defined from the triangle. The points are : The midpoint of each side of the triangle The foot of each altitude The midpoint of the line segment from each vertex of the triangle to the orthocenter
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Nine Point Circle
Abigail, Angela, Glen, and Moe
Aim: Learning how to construct a nine point circle
• Do Now: Write down anything you know about a nine point circle.
What is a nine point circle?In geometry the nine point circle is a circle that can be constructed for any given triangle. It is named a nine point circle because it passes through nine significant points that are defined from the triangle.The points are :
• The midpoint of each side of the triangle• The foot of each altitude
• The midpoint of the line segment from each vertex of the triangle to the orthocenter
What is a nine point circle?The nine point circle is also known as:
• Feuerbach's circle• Euler's circle• Terquem's circle• the six-points circle• the twelve-points circle• the n-point circle• the medioscribed circle• the mid circle• the circum-midcircle
Constructing a nine point circle Step One:
Draw a Scalene triangle and label it
ABC Step Two:
Find the midpoints of ABC
Step Three: Find the altitudes of
ABC
Constructing a nine point circle (ctd)
Step Four:Find the midpoints of
each line segmentStep Five:
Notice the six points lie in a circle
