2026 · Q50
ABC is an equilateral triangle. Let PQRS be a square inscribed in it such that P is on AB and Q is on AC. Which of the following is/are correct?
I. AP:PB = 4:3
II. √3 AB = (2 + √3) PQ
Select the answer using the code given below:
Elementary MathematicsGeometry: Lines, Angles and Triangles
- AI only
- BII only
- CBoth I and II
- DNeither I nor II
Explanation
Let the square have side u; PQ‖BC makes ΔAPQ equilateral, so AP=u. The altitude gives s√3/2=u+u√3/2, i.e. √3·AB=(2+√3)PQ — II is correct. But AP:PB=u:(s−u)=√3:2≈0.866, not 4:3 — I is incorrect. Only II is correct, option B.