if a chord passes through point of reverse curve are the central angles always equal?

[SGCivil]

if a chord passes through point of reverse curve are the central angles always equal?

I am looking this problem and that is was the solution says but it doe not make sense to me. Can someone please explain why this is so?

 

[ptatohed]

SGC, your attachment is too small for me to read the numbers but it appears that R1 equals R2?  Is that correct? 

There are two kinds of reverse curves - those with parallel tangents and those with diverging tangents.  It appears we have a parallel tangent RC in this case.

Thus, if R1 = R2, then I1 must = I2.

 

[youngmotivatedengineer]

ptatohed, as mentioned in the graphic you posted, it's important to note that the angles are equivalent if the PRC is at the midpoint. If the PRC was not at the midpoint of the tangents, the angles would be different.  In the original post, the PRC is at the mid-point so the angle are equivalent.

During the ASCE review courses, they like to point out possible "distractors" in the answer choices.  This seems like it could be a good opportunity for a distractor where people may automatically assume its the same angle, but they may have the PRC at a point other than the midpoint. 

 

[ptatohed]

ptatohed, as mentioned in the graphic you posted, it's important to note that the angles are equivalent if the PRC is at the midpoint. If the PRC was not at the midpoint of the tangents, the angles would be different.  In the original post, the PRC is at the mid-point so the angle are equivalent.

During the ASCE review courses, they like to point out possible "distractors" in the answer choices.  This seems like it could be a good opportunity for a distractor where people may automatically assume its the same angle, but they may have the PRC at a point other than the midpoint. 

This is true but I started with assuming that R1 = R2.  I can't quite read SGC's little figure but I think it looks like R1 = R2?  1780 FT??  If R1 = R2, then L1 = L2 and the PRC will be at the midpoint.  Right?

 

[SGCivil]

thank you. Yes the R's are equal.  This photo may be clearer to see

 

[youngmotivatedengineer]

This is true but I started with assuming that R1 = R2.  I can't quite read SGC's little figure but I think it looks like R1 = R2?  1780 FT??  If R1 = R2, then L1 = L2 and the PRC will be at the midpoint.  Right?

Yes, you did state that R1=R2. I was pointing it out so that SGC and anybody else looking at this realized that R1=R2, and I1=I2 is not automatic for all parallel tangent curves, only for those who have the PRC at the midpoint which is shown in the sketch for this problem.