Question

Point H is the incenter of triangle ABC. Find BD. a. 7.5 b. 8.5 c. 9.2 d. 9.7

Answer 1

Triangle HDB is a right triangle with 60 & 30 degrees, then it is semi equilateral triangle where  HB= 11 & HD =5.5. Now apply Pythagoras  you will find
DB = 9.526 (there is a mistake in the a,b,c,d)

Answer 2

Check the picture below

notice, using the 30-60-90 rule, since that triangle is a 30-60-90 triangle, we get 11 = 2x