# Inscribed Angle Theorem

## This circle's center is at (0,0) with radius 3. Angle CDE is called an inscribed angle.

For the circle above, move point D anywhere between point C and point E, and observe what happens to angle CDE. Next, move point C OR point E to (0, -3). What is the new measurement of angle CDE?

## The circle's center is at (0, 0) with radius 3. Angle CDE is the inscribed angle, and angle CFE is the central angle.

For the circle above, move point D anywhere between point C and point E, and observe what happens to angle CDE and angle CFE. Next, move either point C to (0, 3) and observe what happens to angle CDE and angle CFE. What relationship do you notice between these two angles? This relationship is known as the **Angle at the Center Theorem**.

## The circle's center is at (0, 0) with radius 3. Pay close attention to angle CDE and angle CFE.

## For the circle above, angle CDE is 45 degrees.

What do you think the measurement of angle CFE is? Give your best guess.

## The circle's center is at (0, 0) with radius 3. Pay close attention to angle CDE and angle CFE.

For angle CDE, point D is the

**apex point**and points C and E are the**end points**. For angle CFE, point F is the**apex point**and points C and E are the**end points**. Try moving the apex points and observe what happens to angle CDE and angle CFE. Next, try moving the end points and observe what happens to angle CDE and angle CFE. The**Angles Subtended on the Same Arc Theorem**states that any angles formed by the two same**end points**will have the same measurement.Let's work on some practice problems.

## 1.) The circle's center is at (0, 0) with radius 4.

What is the measurement of angle CFE?

## 2.) The circle's center is at (0, 0) with radius 5.

What is the measurement of angle CFE?