1. Inscribed Angles May 13, 2008

2. What is an inscribed angle? • An inscribed angle is an angle whose vertex is on a circle and whose sides contain chords of the circle. We say that angle 1 above intercepts the arc shown in red.

3. Measure of an inscribed angle • Theorem: The measure of an inscribed angle is equal to half the measure of its intercepted arc.

4. More about inscribed angles

5. Proving the measure of an inscribe angle • Try this one…

6. 1st Corollary • Corollary 1: If two inscribed angles intercept the same arc, then the angles are congruent.

7. 2nd Corollary • Corollary 2: An angle inscribed in a semicircle is a right angle.

8. 3rd Corollary • Corollary 3: If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

9. Angles formed by a chord and a tangent • Theorem: The measure of an angle formed by a chord and a tangent is equal to half the measure of the intercepted arc.

10. More about chords • Theorem: The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs.

11. Secants and tangent • Theorem: The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs.

12. Two secants

13. Two tangents..

14. A tangent and a secant