Construct a Nine-Point Circle

New York State Common Core Math Geometry, Module 1, Lesson 32

Student Outcomes

• Students learn to construct a square and begin to construct a nine-point circle.

Construct a Nine-Point Circle

Classwork

Opening Exercise

During this unit we, have learned many constructions. Now that you have mastered these constructions, write a list of advice for someone who is about to learn the constructions you have learned for the first time. What did and did not help you? What tips did you wish you had at the beginning that would have made it easier along the way?

Exploratory Challenge 1

Yesterday, we began the nine-point circle construction. What did we learn about the triangle that we start our construction with? Where did we stop in the construction?

We continue our construction today.

There are two constructions for finding the center of the nine-point circle. With a partner, work through both constructions.

Construction 1

1. To find the center of the circle, draw inscribed β³ πΏππ.
2. Find the circumcenter of β³ πΏππ, and label it as π.

Recall that the circumcenter of a triangle is the center of the circle that circumscribes the triangle, which, in this case, is the nine-point circle.

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