1975 AMC 12 Question 24 - thichhoctoan.com

Question 24

In triangle $ABC,$ $\angle C=\theta$ and $\angle B=2\theta,$ where $0^\circ\lt\theta\lt60^\circ.$ The circle with center $A$ and radius $AB$ intersects $AC$ at $D$ and intersects $BC,$ extended if necessary, at $B$ and at $E$ ($E$ may coincide with $B$). Then $EC=AD$

for no values of $\theta$
only if $\theta=45^\circ$
only if $0^\circ\lt\theta\le45^\circ$
only if $45^\circ\le\theta\lt60^\circ$
for all $\theta$ such that
$0^\circ\lt\theta\lt60^\circ$