Warm up 30  80  100  180  100  260 . Inscribed Angles and Inscribed Quadrilaterals.

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Presentation transcript:

Warm up 30  80  100  180  100  260 

Inscribed Angles and Inscribed Quadrilaterals

Central Angle Central Angle = Arc

Inscribed Angle Angle where the vertex is ON the circle

Inscribed Angle Inscribed Angle = intercepted Arc/2

160  80  The arc is twice as big as the angle!!

Inscribed angles

120  x y Find the value of x and y.    = 120  = 60 

Examples 1. If m JK = 80  and  JMK = 2x – 4, find x. M Q K S J 2. If m  MKS = 56 , find m MS. x = 

If two inscribed angles intercept the same arc, then they are congruent.  BAD =  BCD A B C D

Find the measure of  DOG,  DIG,  ODI and  OGI D O G I

If all the vertices of a polygon touch the edge of the circle, the polygon is INSCRIBED and the circle is CIRCUMSCRIBED.

Quadrilateral inscribed in a circle: opposite angles are SUPPLEMENTARY A B C D

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

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

4x – 14 = 90 H K G N Example 4 In  K, GH is a diameter and m  GNH = 4x – 14. Find the value of x. x = 26 4x = 104

z 2x x x – 6 = 180 x = 7 z + 85 = 180 z = 95 Example 5 Solve for x and z. 22x – 6 24x +12 = x = 168

Textbook p. 420 #2 – 13 (omit #6), 17 – 20, 22