Warm up X = 6 X = 5.4 X = 20.8 X = 5X = 10

A little extra information ♥The word tangent comes from the Latin word meaning to touch ♥The word secant comes from the Latin word meaning to cut.

Inscribed Angles An angle whose vertex is on the circle is an inscribed angle. Intercepted arc m  B = ½ m AC B C A  If <B = 25°, find mAC  mAC = 50°  An inscribed angle can be created by 2 chords or a tangent and a chord. The measure of an inscribed angle is half the measure of the intercepted arc. A B C m<A = ½ BA  m<A = ½ BCA or 

Let’s Practice a° = 120° b° = ( )/2 = 150/2 = 75°

Let’s go again m<B =(64+90)/2 = 77° m<A = 190/2 = 95° m<C =(106+64)/2 = 85° m<D =(206)/2 = 103° Check your work…. do the measures add to 360 °?

Think about this… What is the relationship between two angles that intercept the same arc? What would be the measure of an angle inscribed in a semicircle? A B x°

Think about this… What is the sum of opposite angle measures in an inscribed quadrilateral? A B

Let’s Practice 154° 27° 76° 105° 100° 38° 90° 52° 104°

Just 2 more 75° 60° 120° 90° 47° 94° 43° <b ҂ <c

Last minute cheat sheet… When 2 lines intersect INSIDE a circle, the measure of the angle formed by them is half the SUM of the measures of the intercepted arcs. When 2 lines intersect OUTSIDE a circle, the measure of the angle formed by them is half the DIFFERENCE of the measures of the intercepted arcs.

Segment Lengths

Your assignment 12.3 Practice – Inscribed Angles 12.4 Practice – Angle Measures and Segment Lengths (extra credit) Abstract Beauty (the last project piece)