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mach5 · Apr 16, 2009, 11:32 PM

A wheel is placed against a wall. One point on the edge of the wheel is 5 inches from the ground and 10 inches from the wall. What is the radius of the wheel?

colbtech · Apr 17, 2009, 12:59 AM

Got the answer, but I drew the wheel/wall in Visio and just increased the size of the wheel until the circumference crossed at 5" high, 10" from wall.

Don't think that's the way to do this problem. Maybe one of the maths guys on here will explain the process.

galactus · Apr 17, 2009, 04:58 AM

Since the point (10,5) is on the circle, use the circle equation:

$(10-r)^{2}+(5-r)^{2}=r^{2}$

$2r^{2}-30r+125=r^{2}$

$r^{2}-30r+125=0$

Solve the quadratic for r. There will be two solutions but only one will make sense.

Capuchin · Apr 17, 2009, 05:28 AM

Gal, why can't both answers be correct?

I worked the lower root of the quadratic out just by observation. (that is, the 2:1 ratio means that the point is d away from the wall and r away from the floor, i.e. on the other side of the wheel from the point it touches the wall).

Am I missing something about one of the solutions?

galactus · Apr 17, 2009, 05:37 AM

5 does not work as a radius because (10,5) would not be on the circle. Or am I having a brain fart?:)

Capuchin · Apr 17, 2009, 05:41 AM

Originally Posted by galactus

5 does not work as a radius because (10,5) would not be on the circle. Or am I having a brain fart?:)

I think so, 10,5 is from the origin, not from the center of the circle (which would be at 5,5 in that case). 10,5 would not be on a circle of radius 25, either if measured from the center!

galactus · Apr 17, 2009, 06:05 AM

Think about it for a second. I think 25 works because if the radius were 5, then x=10 would be too large for it to touch the wall. Anyway, I am going with r=25.

HelpinHere · Apr 17, 2009, 06:11 AM

Well, I just drew it out, and I got BOTH circles as possibilities, with radius 5 and 25, so it *could* be either... unless the OP left out some information.

colbtech · Apr 17, 2009, 06:18 AM

This is what I got and can see the 2 possibilities

Capuchin · Apr 17, 2009, 06:22 AM

Originally Posted by colbtech

This is what I got and can see the 2 possibilities

Exactly what I was thinking.

galactus · Apr 17, 2009, 06:28 AM

Oh, I see, I was picturing something different. I humbly acquiesce and eat crow.

galactus · Apr 17, 2009, 06:35 AM

With other problems I have seen like this, I believe they are referring to the wheel like this and not with the point touching from the other side as in the 5 inch case. But, they both do work, so it is a matter of interpretation.