Question 1178913
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Extend segment EX to meet BC at Y.<br>
By symmetry, Y bisects BC, so CY=6.<br>
Let x be the length of congruent segments BX, CX, and EX; then XY=12-x.<br>
Use the Pythagorean Theorem on triangle CYX to get an equation that is easily solved for x, which is what the problem asks you to find.<br>
I leave the work to you.<br>