Sect. 10.3 Inscribed Angles

1. Sect. 10.3 Inscribed Angles Goal 1 Using Inscribed Angles Goal 2 Using Properties of Inscribed Angles.

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

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

4. Using Inscribed Angles Theorem 10.8 – Measure of an Inscribed Angle 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

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

6. Using Inscribed Angles Example 2: Find the measure of each arc or angle. Q 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 PolygonA polygon whose vertices lie on the circle. Quadrilateral ABFE is inscribed in Circle O.

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

12. Using Inscribed Angles Example 5: FindmEFD

13. Using Properties of Inscribed Angles Theorem 10.10 A triangle inscribed in a circle is a right triangle if and only if one of its sides is a diameter. 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 Theorem 10.11 If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

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

16. Using Properties of Inscribed Angles Find x and y

17. Homework:work sheet will be provided in class