Question 1103311
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From the given information, we can see that triangle ADH is a right triangle with right angle at H, and with DH=4 and AD=8.  That makes it a 30-60-90 right triangle, with AH=4*sqrt(3).<br>
Since AL is the angle bisector, angle A is 60 degrees.<br>
That means triangles AHC, CHB, and ACB are all 30-60-90 right triangles.<br>
{{{AH=4*sqrt(3)}}}, so {{{HC= (4*sqrt(3))*sqrt(3) = 12}}}, so {{{BC = 12*2 = 24}}}