Question

Task 3

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Circle Theorems

In this unit, you learned about some of the important properties of circles. Let’s take a look at a property of circles that might be new to you.

You will use GeoGebra to demonstrate a theorem about chords and radii. Open GeoGebra, and complete each step below.

Part A

Construct a circle of any radius, and draw a chord on it. Then construct the radius of the circle that bisects the chord. Measure the angle between the chord and the radius. What can you conclude about the intersection of a chord and the radius that bisects it? Take a screenshot of your construction, save it, and insert the image below your answer.

Part B

Write a paragraph proof of your conclusion in part A. To begin your proof, draw radii OA and OC.

Part C

In this part of the activity, you will investigate the converse of the theorem stated in part A. To get started, reopen GeoGebra.

Draw a circle of any radius, and draw a chord on it. Construct the radius of the circle that is perpendicular to the chord. Measure the line segments into which the radius divides the chords. How are the line segments related? What can you conclude about the intersection of a chord and a radius that is perpendicular to it? Take a screenshot of your construction, save it, and insert the image below your answer.

Part D

Write a paragraph proof of your conclusion in part C. To begin your proof, draw radii OA and OC .

Answer 1