its on page 21,# 26 the one with the circle. please help.
Let Q be the circle's center.
Draw CQ, AQ, BQ, and AB. Label AQ and BQ with length of 2.
As <AQB is a central angle, it's measure will be the same as arc AB.
We know that the exterior angle is equal to one half the difference of the two intercepted arcs.
50 = (0.5)(big arc - little arc)
We also know that the big arc and little arc sum to 360. so big arc = 360 - little arc.
50 = (0.5)(360 - little arc - little arc)
50 = (0.5)(360 - m of arc AB)
100 = 360 - mAB
-260 = -mAB
130 is the measure of arc AB.
Ok, so if you drew in the segments above, there are two right triangles inside your circle with length 2 for the hypoteneuses. You also now know that one of the angles in the triangle is 65 degrees.
From here, you can use trig to find the side you want, and then double it to know the length of segment AB.