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Geometry - Circles and Chords

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by GmatMathPro » Sun Nov 06, 2011 9:19 am
Ans: E. e and j

Imagine you're walking around this decagon counter-clockwise. As you walk down chord j, you have to make a 35 degree turn to get to chord i. Then you have to make a 32 degree turn to get to chord h. But now, you're facing in the same direction as if you had just made a 32+35=67 degree turn from chord j. As you continue to walk from chord to chord, the degrees of your turns continue to add up, so going all the way from j to e, you have to turn 35+32+45+36+32=180 degrees. So, you are on a different spot on the decagon, but you've essentially turned 180 degrees when you walk on chord e compared to when you were walking on chord j, so the chords are parallel. Note that this kind of reasoning can be used to show that the exterior angles of a polygon add up to 360: if you go all the way around the polygon, you're back facing the way you were at the beginning, so you've made one full 360 degree turn.
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