Warmup Find the measure of each arc Homework

Warm-up Find the measure of each arc.

Homework Review

EOCT Review A gazebo is to be constructed between three houses so that it will approximately be the same distance from each house. Which would be helpful in deciding where to locate the gazebo? a) Centroid b) Circumenter c) Incenter d) Orthocenter b

CCGPS Geometry Day 21 (9 -5 -13) UNIT QUESTION: What special properties are found with the parts of a circle? Standard: MMC 9 -12. G. C. 1 -5, G. GMD. 1 -3 Today’s Question: How do we use angle measures to find measures of arcs? Standard: MMC 9 -12. G. C. 2

Inscribed Angles

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 D TE 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… 160 80

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 inscribed 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. Find the value of x. Q 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.

2 Column Proof

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

Example 6 In K, GH is a diameter and 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 x = 11 K G 1 2 H N

Homework: • Worksheet