Unit Question: What happens when line segments intersect a circle? Today’s Question: What is an inscribed angle and how do you find it’s measure?

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Presentation transcript:

Unit Question: What happens when line segments intersect a circle? Today’s Question: What is an inscribed angle and how do you find it’s measure?

Something to remember: When naming an angle using 3 letters, the letter in the middle is the vertex! D G O

105  120  A B C D R

Inscribed Angle: An angle whose vertex is on the circle and whose sides are chords of the circle INSCRIBED ANGLE INTERCEPTED ARC

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. C L O T 1. YES CL

Determine whether each angle is an inscribed angle. Name the intercepted arc for the angle. Q R K V 2. NO QVR S

120 x What do we call this type of angle? What is the value of x? y What do we call this type of angle?How do we solve for y? The measure of the inscribed angle is HALF the measure of the intercepted arc!!

160  80  To find the measure of an inscribed angle…

Examples 3. If m JK = 80 , find m  JMK. M Q K S J 4. If m  MKS = 56 , find m MS. 40  112 

48º L F A K Find the measure of arc AL. (think about it!)

72  If two inscribed angles intercept the same arc, then they are congruent.

Example 5 In  J, m  3 = 5x and m  4 = 2x + 9. Find the value of x. 3 Q D J T U 4 x = 3

180  diameter If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.

H K G N 4x – 14 = 90 Example 6 In  K, GH is a diameter and m  GNH = 4x – 14. Find the value of x. x = 26

H K G N 6x – 5 + 3x – 4 = 90 Example 7 In  K, m  1 = 6x – 5 and m  2 = 3x – 4. Find the value of x. x =

A circle can be circumscribed around a quadrilateral if and only if its opposite angles are supplementary. A B C D

z y y+6 =180 y = 64 z + 85 = 180 z = 95 Example 8 Find y and z y=180