If pointpis on line R, what is the total number of points 3 centimeters from pointpand 4 centimeters from line R?

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- Oct 14th 2008, 10:04 PMmagentaritaTotal Number of Points
If point

*p*is on line R, what is the total number of points 3 centimeters from point*p*and 4 centimeters from line R? - Oct 14th 2008, 11:12 PMearboth
All points which have a distance of 3 cm from point p are placed on a circle around p with radius r = 3 cm.

All points which have the distance of 4 cm from the line R are placed on 2 parallels of R with a perpendicular distance of 4 cm.

The parallels and the circle don't have common points because the radius is smaller than the perpendicular distance.

Therefore the answer is zero. - Oct 15th 2008, 10:16 AMmasters
Actually, if you constructed four 4 cm tangents from line R to the circle, the 4 points of tangency, A, B, C, D would be 4 cm from line R and also 3 cm from P (making 3 - 4 - 5 right triangles). See diagram. Granted, the distances to R are not perpendicular, but the instructions didn't say they had to be. We're just looking for all the points that are both 3 cm from P and 4 cm from line R. So these 4 points meet the conditions.

And as I look further, any point along the arc AB and arc CD with the exception of the intersection points of line R and the circle can be made to be 3 cm from P and 4 cm from line R. So my reasoning may be flawed. Otherwise, there's an infinite number of points that satisfy the condition specified. - Oct 16th 2008, 07:15 PMmagentaritaok...
- Oct 16th 2008, 07:16 PMmagentaritaok.....
- Oct 16th 2008, 08:19 PMmasters
- Oct 17th 2008, 03:32 AMmagentaritabut...
- Oct 17th 2008, 05:11 AMmasters
I agree with zero. I just created a situation to fit the problem and I didn't use perpendicular distances. What I demonstrated was the fact that there exists more points that are 3cm from P and also 4 cm from a

on line R, not necessarily perpendicular to line R.__point__ - Oct 17th 2008, 01:07 PMmagentaritaI see.....
- Oct 17th 2008, 02:37 PMCaptainBlack