Hard Sat math problem

<p>Practice test 9, section 5, #20: If the give line segments in the figure above are all congruent, what is the ratio of the length of AC(not shown) to the length of BD?</p>

<p>what is the source?</p>

<p>BB, newest edition</p>

<p>eh.</p>

<p>This is my thought process:</p>

<p>It said all sides are congruent, therefore the triangle formed by D, B, and C is equilateral.
AC bisects angle C, and forms a 90 degree angle with DB, therefore 180-90-30=60 and the triangle formed by D, C, and the midpoint of DB (which we'll call E) is a 30-60-90 triangle.</p>

<p>So</p>

<p>DE equals X and CE equals sqroot(3)*X. We're looking to find the ratio of AC to DB. Since both are CE and DE, respectively, multiplied by two, their ratio is going to be the same. Answer choice B.</p>

<p>Got it?</p>