1 Sect Inscribed Angles Goal 1 Using Inscribed Angles Goal 2 Using Properties of Inscribed Angles.

2 Using Inscribed Angles An INSCRIBED ANGLE is an angle whose vertex is on the circle and whose sides each contain chords of a circle. Inscribed Angles & Intercepted Arcs

3 Using Inscribed Angles INSCRIBED angle Central angle Vertex on circle Vertex on center Difference between inscribed angles and Central angles:

4 Using Inscribed Angles If an angle is inscribed in a circle, then the measure of the angle equals one-half the measure of its intercepted arc. m  = m arc OR 2 m  = m arc Theorem 10.8 – Measure of an Inscribed Angle

5 Using Inscribed Angles Example 1: 63  Find the m  PAQ and.

6 Using Inscribed Angles Find the measure of each arc or angle. Example 2: QQ RR

7 Using Inscribed Angles Theorem 10.9 If two inscribed angles intercept the same arc or arcs of equal measure then the inscribed angles have equal measure. m  ACD = m  ABD

8 Using Inscribed Angles Example 3: Find

9 Using Properties of Inscribed Angles Example 4: Find m  CAB and m

10 Using Properties of Inscribed Angles Inscribed Polygon A polygon whose vertices lie on the circle. Quadrilateral ABFE is inscribed in Circle O.

11 Using Properties of Inscribed Angles A polygon is circumscribed about a circle if and only if each side of the polygon is tangent to the circle. Circumscribed Polygon

12 Using Inscribed Angles Example 5: Find m  EFD

13 Using Properties of Inscribed Angles A triangle inscribed in a circle is a right triangle if and only if one of its sides is a diameter. Theorem  A has its vertex on the circle, and it intercepts half of the circle so that m  A = 90.

14 Using Properties of Inscribed Angles If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary. Theorem 10.11

15 Using Properties of Inscribed Angles Find the measure of Example 6: Find x.

16 Using Properties of Inscribed Angles Find x and y

17 Homework:work sheet will be provided in class