How does the larger semicircle have twice the radius?

[The Blade Dancer]

Module 2 Week 1 Day 3 Your Turn Part 3

How does the larger semicircle have twice the radius? It all looks the same to me.

Also in C4 the forum link does not need to be accessed by answering the question first if you look at it, unlike the others. Bug?

[nastya]

Hi @The-Darkin-Blade,

The large semicircle is the one that is purple and goes through all four vertices of the trapezoid. This purple semicircle, as we
see on the picture, has radius \({\color{purple}\bf{2r}},\) whereas the smaller semicircle is the one that is light-orange with diameter the side of our trapezoid. This orange semicircle, as we can see in the picture, has radius \({\color{darkorange}\bf{r}}.\) So, the larger semicircle has twice the radius of the smaller one.

About the forum link in C4, thank you for mentioning this! We've fixed the link so that it matches the other lessons, so it can now be found after the mini-question explanation.

[RZ923]

@The-Blade-Dancer
I think earlier in this module Prof Loh proved that a hexagon can be made of 6 equilateral congruent triangles.
So the \(r\) is half the side length of the triangles, and \(2r\) is the length of the triangle.