VTMO 2026 - Grade 9 - Semifinal - SET 07 - Self-study Question 3

Question 3

Triangle $ABC$ has $\angle ACB=45^\circ$. Construct an isosceles right triangle $ACI$, right-angled at $C$, outside $ABC$. Let $E=AC\cap BI$. If $BI=\sqrt2\,BC$, find $AE/CE$.

$2/3$
$3/4$
$\sqrt3-1$
$\sqrt2/2$
1