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Inscribed angles 10-4

Topic:
Angles

Find the measure of arc CD.

An inscribed angle is an angle whose vertex is on the circle. This task will help us understand how to calculate the measure of the inscribed angle.

What is the ratio of Angle CED to Arc CD? Move points C, D, and E around the circle to see if that ratio stays constant.

Based on the construction and the previous question what can we state about the measure of an inscribed angle?

In this task we are going to study the relationship between the opposite angles of an inscribed quadrilateral.

What is the relationship between the opposite angles of the inscribed quadrilateral? Move the vertices of the quadrilateral around to make sure that relationship is constant.

This task we will study one feature of an inscribed right triangle. Move the slider to adjust angle D. Do you see anything special?

What do notice when the triangle becomes a right triangle?

What is the measure of angle DCE?

What is the measure of angle DEC?

What is the measure of angle DCE?

What are the measures of angles F and E?