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Topic: A circle with center O (Read 555 times) |
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tony123
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A circle with center O
« on: Oct 4th, 2007, 2:58am » |
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A circle with center O and radius 1 cm rolls around the inside of a triangle whose sides are 6, 8, and 10 cm, always touching one or more of the sides as it rolls. How far does O travel in one complete circuit?
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towr
wu::riddles Moderator
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Some people are average, some are just mean.
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Re: A circle with center O
« Reply #1 on: Oct 4th, 2007, 5:56am » |
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Seems easy to me, you can just shave the edges off, then walk around the perimeter as a point.
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FiBsTeR
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Re: A circle with center O
« Reply #2 on: Oct 4th, 2007, 6:25pm » |
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If the original triangle has vertices {(0,0),(0,6),(8,0)}, then O will travel along the perimeter of the triangle with vertices {(1,1),(1,[21/4]),([20/3],1)}; this perimeter is equal to 17.
EXTENSION: Let A be the original triangle above, with vertices at {(0,0),(0,6),(8,0)}, and B be the triangle with vertices at {(1,1),(1,[21/4]),([20/3],1)}. Suppose point P starts at (0,0) on A and point Q starts at (1,1) on B, both moving 1/12 unit per second clockwise around the perimeter of their respective triangles. How much time will elapse until both points are once again on a vertex of their triangles at the same time?
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| « Last Edit: Oct 5th, 2007, 2:08pm by FiBsTeR » |
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FiBsTeR
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Re: A circle with center O
« Reply #3 on: Oct 8th, 2007, 11:18am » |
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Well, since this got buried unanswered, the answer to my question was 1224 seconds or 20.4 minutes. 
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