If you want to construct a circle that touched each of the corners of a triangle, what should you construct?

Consider a cube that has sides of length l. now consider putting the largest sphere you can inside this cube without any point on the sphere lying outside of the cube. the volume ratio -volume of the sphere/ volume of the cube is 1. 5.2 × 10−1 2. 3.8 × 10−1 3. 1.9 4. 2.5 × 10−1 5. 3.8

What are the triple angle formulas? is it related to double angle identities?

Find the measure of the missing angle