10.4 Inscribed Angles

Definition of Inscribed Angles An Inscribed angle is an angle with its vertex on the circle.

Theorem An Inscribed angle equals half the intercepted arc.

Theorem Practice Problem An Inscribed angle equals half the intercepted arc. ADC = 180°

Theorem Practice Problem An Inscribed angle equals half the intercepted arc. ADC = 240°

Theorem If two inscribed angles have the same intercepted arc, then the angles are equal.

Some Definitions A polygon whose vertices are touching a circle is called inscribed. If a Circle is drawn around a polygon, it is circumscribed about the circle.

Theorem If a right triangle is inscribed in a circle, the hypotenuse is the diameter.

Theorem A Quadrilateral can be inscribed in a circle if and only if opposite angles are supplementary.

You try these: State the theorem. 1. Solve for x

2. Solve for x

3. Solve for x, y and z

4. Solve for x and y

5. Solve for x and y

6. Solve for x and y

Solve for x and y

Solve for x and y