Lesson 10-4: Inscribed Angles

Lesson 10-4: Inscribed Angles Inscribed Angle: An angle whose vertex lies on a circle and whose sides are chords of the circle (or one side tangent to the circle). Examples: 3 1 2 4 No! Yes! No! Yes! Lesson 10-4: Inscribed Angles

Lesson 10-4: Inscribed Angles Intercepted Arc Intercepted Arc: An angle intercepts an arc if and only if each of the following conditions holds: 1. The endpoints of the arc lie on the angle. 2. All points of the arc, except the endpoints, are in the interior of the angle. 3. Each side of the angle contains an endpoint of the arc. Lesson 10-4: Inscribed Angles

Lesson 10-4: Inscribed Angles Inscribed Angle Theorem The measure of an inscribed angle is equal to ½ the measure of the intercepted arc. Y Inscribed Angle 110 55 Z Intercepted Arc An angle formed by a chord and a tangent can be considered an inscribed angle. mAB 2 mABC = or 2 (mABC ) = mAB Lesson 10-4: Inscribed Angles

Lesson 10-4: Inscribed Angles Examples: Find the value of x and y in the fig. y ° x 50 A B C E F y ° 40 x 50 A B C D E Lesson 10-4: Inscribed Angles

Lesson 10-4: Inscribed Angles An angle inscribed in a semicircle is a right angle. P 180 90 S R Lesson 10-4: Inscribed Angles

Inscribed Quadrilaterals If a quadrilateral is inscribed in a circle, then the opposite angles are supplementary. mDAB + mDCB = 180  mADC + mABC = 180  Chapter 10-6: Interior and Exterior Angles