## Online Course Discussion Forum

### 2021 AMC 12 Intensive Prep Questions

I was reviewing past questions for Math Challenge II-B Geometry and had some questions on Chapter 9. Specifically for questions 9.25 and 9.26. For question 9.25, I understand the solution given, but don’t understand why my attempt doesn’t work. The image attached is what I’ll use as my reference for explaining what I did. First, the radius of the sphere, 1, is the length of OD. I assumed ODH was a 30,60,90 triangle because this was a regular tetrahedron, meaning each of its bases is an equilateral triangle. Through that, I used the 30, 60, 90 relationships to find the length of HD, which was 32. I then took into consideration the equilateral triangle BCD, creating the points in the second image attached. X, Y, and Z are midpoints and the relationship with these lines creates HDX as another 30,60,90 triangle. With this, I found the length of DX, which was 3/4. The side length is twice this, which is 3/2. However, this was not the correct answer. For question 9.26, I just don’t understand how to draw this correctly and I kind of need a description or a drawing to understand the solution.

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