I'm hoping that someone can give me some help with the following problem:
O is the centre of the circle (show on the attachment to this post) and AB is parallel to CD. Find the angles labelled x and y.
With a bit of cheating I was able to find that x = 32o and y = 58o but my questions is 'why' or what is the 'proof' of this?
Oct 7th 2013, 05:59 AM
Re: Circles and Angles
If you construct a line from Point B horizontally to intersect DC at right angles at Point E, from symmetry you can see that the length of that line is R sin(64). And from that the angle BDC (which also equals angle x) is arctan(Rsin(64)/(R+Rcos(64)). From that you have angle x.
Length CE is then R-Rcos(64), so angle y is arctan(Rsin(64)/(R-Rcos(64)).