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# In the figure below, a wheel with center O rolls, without

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In the figure below, a wheel with center O rolls, without [#permalink]

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02 Aug 2003, 11:58
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In the figure below, a wheel with center O rolls, without slipping, in a straight line across a level floor. Two spots of wet paint at points A and B on the rim of the wheel leave marks on the floor, as indicated by the dots on the floor. What is the value of x ? ( Note:X is degrees) X is the degree measure of the arc.

7 in | 8 in | 7 in | circle
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Last edited by Curly05 on 02 Aug 2003, 12:48, edited 1 time in total.
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02 Aug 2003, 12:31
The circumference is 8+7=15
I assume that the angle X corresponds to a 7-inch arc.

A proportion: 15/360=7/X

X=168 degrees
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02 Aug 2003, 13:25
I've never seen this before used in geometry.

But, I think I got your idea, Stolyar.
15 inches 7 inches
----------- = ---------
360 degrees x how many degrees in a circle
X= 168.

Let me try to upload the picture. 15 inches should represent a diameter.

The x represents a portion of the degree measure of the semi-circle arc or the diameter
The diameter is 30 inches and represents half the degree measure in a circle. 22 inches so far taken up.
x = 11
--- ----

180 15

168 degrees / 180 degrees or 11/15 of the circumference of the semi-circle is rolled.
Arc Measure = 11/15 * 2 pi r= 30
Arc Measure = 22

The line segment length of 22 corresponds to 11/15 of the circle's circumference. This makes it a classic GMAT Problem.
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Hey Stolyar   [#permalink] 02 Aug 2003, 13:25
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