The diagram shows five equal semicircles and the lengths of some line segments. What is the radius of the semicircles?
A. 12 B. 16 C. 18 D. 22 E. 28
Sat the Intermediate Maths Challenge on Wednesday?
Join a live Zoom session where we’ll go through the hardest problems, discuss solution strategies, and what to focus on next.
📅 Tuesday, 3 February 2026
⏰ 18:30–19:30 (UK time)
💻 Live on Zoom
C
Let the radius of each semicircle be r. From the diagram we can see that 2r +12+2r +12+2r = 22 + 2r + 16 + 2r + 22 and hence 6r + 24 = 4r + 60. Therefore 2r + 24 = 60 and so 2r = 36 and hence r = 18.

This course guides you through the fundamentals of Python programming using an interactive Python library known as Turtle.

This course encompasses a range of Geometry topics such as coordinate and spatial geometry, introductory trigonometry, angles, parallel lines, congruent and similar triangles, polygons, circles, the Pythagorean Theorem, and more. Emphasis will be placed on reinforcing Algebra skills and enhancing critical thinking through problem-solving in both mathematical and real-world contexts.

Ask about our courses and offerings, and we will help you choose what works best for you.