Problem
GEO-B2-M05-P008 Radius of the Image of a Line
#8
★★★☆☆ Level 3 of 5
An inversion has radius \(10\). Line \(l\) is at distance \(5\) from centre \(O\). Find the radius of the circle into which \(l\) maps.
The image has diameter \(OH'\), where \(OH\cdot OH'=R^2\).
Here \(OH=5\), so \(OH'=\frac{100}{5}=20\). The image of the line is the circle with diameter \(OH'\), hence its radius is \(10\).
A computation after the lemma on the image of a line.