10.5 Angles Related to a Circle!

Hi! Today in class we learned about angles related to circles.
Here are the theorems!

  The first theorem has to do with inscribed angles.The measure of an inscribed angle (vertex of a circle) is one-half the measure of its intercepted arc.                                                  1/2a=x 



Next we have a chord-chord angle        The meaure of a chord-chord angle is one-half the sum of the measures of the arcs intercepted by the chord-chord angle and its vertical angle    

x=1/2(a+b)

 The next angle is a tangent-chord angle.     The measure of a tangent-chord angle is one-half the measure of its intercepted arc.

1/2a=x

 This is a secant-secant angle.  The measure of a secant-secant angle is one-half the difference of the measures of the intercepted arcs.

x=1/2(a-b)

Now we have a secant-tangent angle. The measure of a secant-tangent angle is one-half the difference of the measures of the intercepted arcs.

x=1/2(a-b)

Finally, we have a tangent-tangent angle.  The measure of a tangent-tangent angle is one-half the difference of the measures of the intercepted arcs.

x=1/2(a-b)

                                   

So, in conclusion:

chord-chord angles.........x=1/2(a+b)

inscribed angles or tangent-chord angles..........x=1/2a

tangent-tangent angles, tangent-secant angles, or secant-secant angles............x=1/2(a-b)

Here are some helpful websites:

http://library.thinkquest.org/20991/geo/circles.html

http://www.regentsprep.org/Regents/math/geometry/GP15/CircleAngles.htm

And you can watch a video where a guy solves a problem with them by clicking

Here!

Bye, Hope I helped :D

~Katie