Inscribed Angles and its Intercepted Arc.pptx

about inscribed angles and its intercepted arc

1. PREPARED BY: Sheila b. bacolod

2. OBJECTIVES: • Understand and apply the concept of an inscribed angle of a circle. • Familiarize the ways on how to solve the inscribed angle and its arc. • To solve the given measure of an inscribed angle and its arc.

3. INSCRIBED ANGLES AND ARCS

4. An  inscribed angle  is an angle with its vertex on the circle and whose sides are chords. The  intercepted arc  is the arc that is inside the inscribed angle and whose endpoints are on the angle.

5. Inscribed Angle Theorem  states that the measure of an inscribed angle is half the measure of its intercepted arc. m ∠ ADC = ½ m A͡C and m A͡C = 2m ∠ ADC

6. Congruent Inscribed Angles Theorem are inscribed angle that intercept the same arc are congruent. ∠ ADB   and   ∠ ACB   intercept A͡B , so   m ∠ ADB = m ∠ ACB . Similarly,   ∠ DAC   and   ∠ DBC   Intercept D͡͡C , so   m ∠ DAC = m ∠ DBC .

7. An angle intercepts a semicircle if and only if it is a right angle ( Semicircle Theorem ). Anytime a right angle is inscribed in a circle, the endpoints of the angle are the endpoints of a diameter and the diameter is the hypotenuse.

8. m D͡C = 2 ( 45˚ ) = 90˚ EXAMPLE: m∠ADB = ½ ( 76˚ ) = 38˚

9. Find  m∠ADB  and  m∠ACB . The intercepted arc for both angles is A͡B. Therefore, m∠ADB = ½ ( 124˚ ) = 62˚ m∠ACB = ½ ( 124˚ ) = 62˚

10. Find  m∠DAB  in ⨀ C. C is the center, so D͞B is a diameter. ∠DAB's endpoints are on the diameter, so the central angle is 180˚. m∠DAB = ½ ( 180˚ ) = 90˚.  

11. TEST YOURSELF: 1. m ∠ABC = 2. m ∠CDE = 3. m ∠ABE = 4. m ∠ACD = 5. m E͡A = A B D C E O 56˚ 104˚