Question

In circle A, m∠AED = 48° and m∠DAE = 44°. Determine if AC=Ef

Answer 1

http://puu.sh/45SM0.png <-- graph of circle

Answer 2

I don't think you will have AC = EF. Notice that AC is a radius of the circle, so AC=AF=AE. Then AC=EF only if we have EF=AF=AE, so the triangle AEF is equilateral. That means the angle AED has to be 60 degrees.

Answer 3

so basically, because its a radius, it means the other two sides of the triangle would have to be the same length, because they are radius's as well, which means that if AC=EF, then EF must also equal AF and AE, correct?

Which would require the triangle to be equilateral.

But how does that mean that AED has to be 60 degrees?

Answer 4

That is all correct.
All interior angles in an equilateral triangle are 60 degrees.

Answer 5

but AED isn't an angle of the equilateral triangle formed by the two non equilateral triangles.

Answer 6

Whoops, sorry i was thinking of DAE

Answer 7

Oh darn, I realised I just read the question completely wrong. What I thought (somehow) was an = sign was infact a perpendicular sign.

So the question here is actually:

In circle A, m∠AED = 48° and m∠DAE = 44°. Determine if AC is perpendicular Ef

Answer 8

Perpendicular bisector*

Answer 9

That question actually makes more sense (since it uses all the numbers). The answer is again no: the line AC will bisect EF only if it bisects the angle EAF. So the angle DAF is also 44 degrees. And since the triangle AEF is isosceles, the angle AFD is equal to AED, so it is 48 degrees.

But this is impossible, since the angles in a triangle must always add up to 180, whereas here the angle add up to 44+44+48+48=184.

Answer 10

Thanks so much!

Just to make sure I'm not crazy, the upside down T symbol does mean perpendicular bisector, right?

Answer 11

Line AC is not a perpendicular bisector of EF.

In order for AC to be a PB of EF, it must also bisect m∠EAF.
If it bisectors m∠EAF, then that means m∠DAE is congruent to m∠DAF.
If m∠DAF is congruent to m∠DAE, then m∠DAF equals 44 degrees.
Triangle m∠AEF is an isosceles triangle, therefor angle m∠AFD is equal to angle m∠AED, so it equals 48 degrees.
Angles of a triangle add up to 180 degrees.
If AC is a perpendicular bisector of EF, then the angles add up to 44+44+48+48 = 184.
This is impossible, therefor AC is not a perpendicular bisector of EF.

Thats what I know so far. That's all correct right?

Answer 12

Yup :)

Answer 13

Thanks a lot Erin001001!