Circles Question (involves point of tangency)

[s3a]

I don't get #9. Please help! (I understand inscribed angles, and that kind of thing but I don't know what to do with the point of tangency.

 

[Loren]

Arcs AB and CD add up to 360° - 80° - 60°. The sum of any two vertical angles at E equals the sum of their intercepted arcs.

 

[fasteddie65]

#9

Arc AC is 88 deg in measure.
So arc BAC = 198. Arc BC = 272. So b = 136 degrees. The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

 

[Mrspi]

#9

Arc AC is 88 deg in measure.
So arc BAC = 198. Arc BC = 272. So b = 136 degrees. The measure of an angle formed by a tangent and a chord is half the measure of the intercepted arc.

Better re-check your arithmetic, Fast one. It's often better to be correct than it is to be fast.

If arc BAC = 198 (which it certainly DOES) AND if arc BC = 272, you've got a circle whose total degree measure is 198 + 272, or 470 degrees!

It might have been helpful, also, to tell WHY arc AC = 88 degrees. If two chords, or a tangent and a chord, intersect at a point ON the circle, then the degree measure of the angle formed is 1/2 the degree measure of the intercepted arc. The intercepted arc is the arc which, except for its endpoints, is in the interior of the angle formed.