05/30/2020 (2011: National Team Round, Problem 6)
Q: Given that m∠A = 60, BC = 12 units, BD ⊥ AC , CE ⊥ AB and m∠DBC = 3m∠ECB, the length of segment EC can be expressed in the form a(√b + √c) units where b and c have no perfect-square factors. What is the value of a + b + c? A: 11