iran-konkur 2023 Q27

iran-konkur · Other · konkur-riazi_1402_general Circles Area and Geometric Measurement Involving Circles
27. In a rectangle, lines from two opposite vertices are drawn perpendicular to a diagonal, and that diagonal is divided into three parts such that the middle part is twice each of the two side parts. The area of this rectangle is how many times the area of the smallest triangle formed inside the rectangle?
(1) $24$ (2) $16$ (3) $12$ (4) $8$
\textbf{27.} In a rectangle, lines from two opposite vertices are drawn perpendicular to a diagonal, and that diagonal is divided into three parts such that the middle part is twice each of the two side parts. The area of this rectangle is how many times the area of the smallest triangle formed inside the rectangle?

(1) $24$ \hspace{2cm} (2) $16$ \hspace{2cm} (3) $12$ \hspace{2cm} (4) $8$