Warm up

X = 6 X = 5.4 X = 20.8

X = 5 X = 10 X = 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

mB = 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° = (120 + 30)/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 °?

Thinkaboutthis…

What is the relationship between two angles that intercept the same arc?

What would be the measure of an angle inscribed in a semicircle?

AB

x°

Thinkaboutthis…

What is the sum of opposite angle measures in an inscribed quadrilateral?

A

B

Let’s Practice

154°

27°

76°

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)