Library / UKMT Intermediate Mathematical Challenge /115 of 267

UKMT Intermediate Mathematical Challenge, 2020

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows two squares and four equal semicircles. The edges of the outer square have length $48$ and the inner square joins the midpoints of the edges of the outer square. Each semicircle touches two edges of the outer square, and the diameter of each semicircle lies along an edge of the inner square. What is the radius of each semicircle?

(A) $10$ (B) $12$ (C) $14$ (D) $16$ (E) $18$

Figure for this problem

We don't reproduce this publisher's solutions. Their own solution is here — work the problem first.

Want a route through all this instead of an archive? The track puts 2,604 problems in a working order, from Junior Challenge level to the IMO shortlist.

Source: UK Mathematics Trust, licensed © UK Mathematics Trust; past papers published free at ukmt.org.uk. Statement reproduced verbatim; metadata (topic, difficulty) added by this project. Solutions are the publisher's, linked not copied.