P, Q and R represent the positions of three radio beacons. P is 450 km from Q, Q is 475 km from R, and R is 300 km P. Signals from P have a range of 300 km, Q has a range of 350 km and R has a range of 200 km. Shade the region in which all three signals can be received. Measure the shortest distance from Q to this region.
Sorry for the confusing title, I don't know the terminology used to describe these types of questions.
Here is my work on Geogebra: https://www.geogebra.org/geometry/gsxvrgzs. The distance I got is 275 km.
Here is the book's answer:
My question: What is causing this difference between my and the book's results? My guess is that the book's diagram is misrepresenting something (or I'm wrong myself).
Edit: I left out a really integral part of the question, sorry.