Problem
GEO-B2-M05-P003 Radius for Swapping Points
#3
★★☆☆☆ Level 2 of 5
Points \(A\) and \(B\) lie on one ray from \(O\), with \(OA=4\), \(OB=25\). Find the radius of the inversion with centre \(O\) sending \(A\) to \(B\).
We need \(R^2=OA\cdot OB\).
We get \(R^2=4\cdot 25=100\), so \(R=10\). Since the points lie on one ray, the inversion condition is fully satisfied.
A standard radius-choice move.