Lesson 3: Midpoint - Circle

   Constructing Knowledge

Unlike other two dimensional shapes, circles do not have any defined sides. As a result the process for finding the midpoint of a circle is unique.

For a circle:

Step 1: Draw a chord inside the circle, and find the midpoint of the chord.

Step 2: Draw a line at a 90° angle through the midpoint of the chord.

Step 3: Draw a second chord inside the circle, and find the midpoint of the second chord.

Step 4: Draw a line at a 90° angle through the midpoint of the second chord.

The midpoint of the circle is where the two lines intersect.

Chord
a straight line that connects two points on a curve

   Multimedia

A video demonstrating finding the midpoint of a circle is provided.

EXAMPLE

Find the midpoint of the circle.



Solution


Step 1: Draw a chord inside the circle, and find the midpoint of the chord.

The chord is 11 cm long, so the midpoint is at 5.5 cm. Mark the midpoint

Hint: a chord can be any length, so move the ruler so that the chord length is a whole number to make finding the midpoint easier.



Step 2: Draw a line at a 90° angle through the midpoint of the chord.

Measure 90° with a protractor



Connect the 90° point with the midpoint of the chord.



Step 3: Draw a second chord inside the circle, and find the midpoint of the second chord.

The second chord is in blue. It is 8 cm long, so the midpoint is at 4 cm. Mark the midpoint.



Step 4: Draw a line at a 90° angle through the midpoint of the second chord.

Measure 90° with a protractor



Connect the 90° point with the midpoint of the chord.



The midpoint of the circle is where the two lines intersect.




Now, it is your turn! Complete the questions in your Chapter 6, Lesson 3 Practice Makes Perfect that refer to Midpoint of Circles.


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