Question 12. The diagram shows 5 equal semicircles and the lengths of some line segments. What is the radius of the semicircles? Let's draw out our shape. It is important to recognize that we can see one continuous line here. Now, all of these circles are equal, so we know that the radius will be the same regardless. To solve this question, first let us cover up half of this. We get 22, a semicircle, 16, a semicircle, and 22 again. So, with this, we know that each semicircle will have a length of 2 times the radius. So we can write out 22 plus 2r plus 16 plus 2r plus 22. Now, let's look at the other side. We have 3 semicircles and 2 twelfths. We will write this out as 2r plus 12 plus 2r plus 12 plus 2r. And since these make up the same line segment in total, we can set these two equations equal to each other. If we simplify this, we get 60 plus 4r equal to 6r plus 24. Simplifying this further, we get 36 equal to 2r. Since we wish to find the radius, we just need to divide 36 by 2, and that will give us our answer, which is C, 18.

semicircles

radius

geometry

equations

solution