Warm up 30 80 100 180 100 260
Review HW
Inscribed Angles and Inscribed Quadrilaterals
Wheel of Formulas!!
Central Angle Angle = Arc
Inscribed Angle Angle where the vertex is ON the circle
Inscribed Angle
160 The arc is twice as big as the angle!! 80
Find the value of x and y. 120 = 120 x y = 60
x = 22 112 Examples 1. If mJK = 80 and JMK = 2x – 4, find x. 2. If mMKS = 56, find m MS. 112 M Q K S J
Find the measure of DOG and DIG 72˚ If two inscribed angles intercept the same arc, then they are congruent. G O 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
If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.
x = 3 5x = 2x + 9 3x = + 9 In J, m3 = 5x and m 4 = 2x + 9. Example 3 In J, m3 = 5x and m 4 = 2x + 9. Find the value of x. 3 Q D J T U 4 5x = 2x + 9 3x = + 9 x = 3
Example 4 In K, GH is a diameter and mGNH = 4x – 14. Find the value of x. 4x – 14 = 90 H K G N 4x = 104 x = 26
Example 5 Solve for x and z. 85 2x +18 + 22x – 6 = 180 24x +12 = 180 22x – 6 24x = 168 x = 7 z + 85 = 180 z = 95
Secant and Tangent Angles Vertex is INSIDE OR OUTSIDE the circle
Vertex is INSIDE the Circle NOT at the Center
Ex. 1 Solve for x 180 – 88 X 88 84 92 x = 100
Ex. 2 Solve for x. 360 – 89 – 93 – 45 45 93 xº 89 133 x = 89
Vertex is OUTside the Circle
Ex. 3 Solve for x. x 15° x = 25 65°
Ex. 4 Solve for x. 27° x 70° x = 16
Ex. 5 Solve for x. 360 – 260 260° 100 x x = 80
Tune: If You’re Happy and You Know It If the vertex is ON the circle half the arc. <clap, clap> If the vertex is IN the circle half the sum. <clap, clap> But if the vertex is OUTside, then you’re in for a ride, cause it’s half of the difference anyway. <clap, clap>