A semicircle has diameter $XY$. A square $PQRS$ with side length 12 is inscribed in the semicircle with $P$ and $S$ on the diameter. Square $STUV$ has $T$ on $RS$, $U$ on the semicircle, and $V$ on $XY$. What is the area of $STUV$?
Problem
Source: Malaysia National Olympiad 2010 Sulung Category Problem 4
Tags: geometry, geometry unsolved
SCP
04.06.2011 16:28
MathSolver94 wrote: A semicircle has diameter $XY$. A square $PQRS$ with side length 12 is inscribed in the semicircle with $P$ and $S$ on the diameter. Square $STUV$ has $T$ on $RS$, $U$ on the semicircle, and $V$ on $XY$. What is the area of $STUV$? Is that for the "big men"? Pythagoras: $r=\sqrt{180}=6\sqrt{5}$ and we get system $(6+x)^2+x^2=180$ That gives solution $x=6$ so area is $36.$
MathSolver94
04.06.2011 18:54
SCP wrote: MathSolver94 wrote: A semicircle has diameter $XY$. A square $PQRS$ with side length 12 is inscribed in the semicircle with $P$ and $S$ on the diameter. Square $STUV$ has $T$ on $RS$, $U$ on the semicircle, and $V$ on $XY$. What is the area of $STUV$? Is that for the "big men"? Pythagoras: $r=\sqrt{180}=6\sqrt{5}$ and we get system $(6+x)^2+x^2=180$ That gives solution $x=6$ so area is $36.$ Big men?
sunken rock
24.02.2014 23:49
google translator says sulung=the oldest (I actually requested the equivalent of my native language, because I only know 'trimakasi'). Best regards, sunken rock