ae = eb = 6x - 10 segment bisector theorem
ce = ed = x² - 3 segment bisector theorem
ce + ed = cd segment addition postulate
x² - 3 + x² - 3 = 66 substitution
2x² - 6 = 66 simplify (added like terms)
2x² = 72 addition property of equality
x² = 36 division property of equality
x = 6 square root property of equality
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ae + eb = ab segment addition postulate
6x - 10 + 6x - 10 = ab substitution
12x - 20 = ab simplify (added like terms)
12(6) - 20 = ab substitution
72 - 20 = ab simplify
52 = ab simplify
Answer: ab = 52
