Question

In circle Q, segment AB is parallel to segment EF and the arcs between segments EF and CD are congruent. Prove that the arcs between segments AB and CD are congruent. If arc AB measures twice that of arc CD and arc AC measures 105 degrees, what is the measure of arc CD?

Answer 1

I don't follow this one... you need to prove that AB and CD are congruent, though the arc of AB measures twice that of CD? ... only possibility here is that AB is 240 and 120...

I can be mistaken though.

Answer 2

This is why I'm confused. My instructor always asks the problems in the most complex of ways.

Answer 3

Well I don't rally understand circles. I did alright with everything else. It's the... roundness... that gets to me. -_-

Answer 4

AB and EF Are parallel so arcs AE and BF are congruent by symmetry - therefore arcs between AB and CD are congruent.

Answer 5

if arc ac = 105 degrees arc AD = 105
so arc AB + arc CD = 360-210 = 150 degrees
so sinc arc AB = 2 x arc CD
arc CD = 150/3 = 50 degrees

Answer 6

typo first line BD = 105

Answer 7

Thank you so much! You're a lifesaver! (Well according to this site, you're a sensei. But you an still be a lifesaver!)

Answer 8

lol - your welcome