Originally Posted by

**masters** 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.