For each circle C find the value of

For each circle C, find the value of x. Assume that segments that appear to be tangent are tangent. 1) 2)

IN Inscribed Angle: An angle whose is on the circle and sides are chords whose the circle of IN SC AN RIB GL ED E ED T EP RC C TE AR vertex

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

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

To find the measure of an inscribed angle… 1600 800

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

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

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

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

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

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

Example 8 Find y and z. z 110 + y =180 y y = 70 z + 85 = 180 z = 95 85

180 er et am di If a right triangle is inscribed in a circle then the hypotenuse is the diameter of the circle.

Example 6 In K, m<GNH = 4 x – 14. Find the value of x. 4 x – 14 = 90 x = 26 H K N G

Example 7 In K, m<1 = 6 x – 5 and m<2 = 3 x – 4. Find the value of x. 6 x – 5 + 3 x – 4 + 90 = 180 or 6 x – 5 + 3 x – 4 = 90 G x = 11 K 1 2 H N