API · no tools. This is the prompt and response recorded for this attempt; a full solution may not have been returned.
This is a Korean CSAT mathematics multiple-choice problem. Solve it and put only the correct choice symbol, one of ①, ②, ③, ④, ⑤, inside \boxed{}.
Problem 28 Consider the tetrahedronABCDwith AB= CD= 4 and BC= BD= 2 √ 5. LetHbe the foot of the perpendicular fromAto lineCD. Suppose that the planesABHandBCD are perpendicular to each other and that AH= 4. LetGbe the centroid of triangleABH, and letSbe the sphere with centerGtangent to the planeACD. LetTbe the locus of all pointsPonSsuch that∠AP G= π 2 . Find the area of the orthogonal projection ofT onto the planeABC. [4 points] ① π 7 ② π 6 ③ π 5 ④ π 4 ⑤ π 3 18 Numerical answer
\boxed{④}
Comparative Analysis (P43) (Average across runs)
Averages use reported measurements only. Missing usage is not treated as zero.