csat-suneung 2025 Q27G

csat-suneung · South Korea · csat__math 3 marks Vectors 3D & Lines Sphere-Plane Intersection and Projection of Circles

As shown in the figure, for a tetrahedron ABCD with $\overline{\mathrm{AB}} = 6$, $\overline{\mathrm{BC}} = 4\sqrt{5}$, let M be the midpoint of segment BC. Triangle AMD is equilateral and line BC is perpendicular to plane AMD. Find the area of the orthogonal projection of the circle inscribed in triangle ACD onto plane BCD. [3 points]
(1) $\frac{\sqrt{10}}{4}\pi$
(2) $\frac{\sqrt{10}}{6}\pi$
(3) $\frac{\sqrt{10}}{8}\pi$
(4) $\frac{\sqrt{10}}{10}\pi$
(5) $\frac{\sqrt{10}}{12}\pi$

As shown in the figure, for a tetrahedron ABCD with $\overline{\mathrm{AB}} = 6$, $\overline{\mathrm{BC}} = 4\sqrt{5}$, let M be the midpoint of segment BC. Triangle AMD is equilateral and line BC is perpendicular to plane AMD. Find the area of the orthogonal projection of the circle inscribed in triangle ACD onto plane BCD. [3 points]\\
(1) $\frac{\sqrt{10}}{4}\pi$\\
(2) $\frac{\sqrt{10}}{6}\pi$\\
(3) $\frac{\sqrt{10}}{8}\pi$\\
(4) $\frac{\sqrt{10}}{10}\pi$\\
(5) $\frac{\sqrt{10}}{12}\pi$

Paper Questions

Q1 Q2 Q3 Q4 Q5 Q6 Q7 Q8 Q9 Q10 Q11 Q12 Q13 Q14 Q15 Q16 Q17 Q18 Q19 Q20 Q21 Q22 Q23 Q23C Q23G Q24 Q24C Q25 Q25C Q26 Q26C Q27 Q27C Q27G Q28 Q28C Q28G Q29 Q29C Q29G Q30 Q30C Q30G