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SMO 2016 Open Round 1 Question 1

SMO · SMO 2016 Open Round 1

Question 1

In this paper, let $[x]$ denote the greatest integer not exceeding x. For examples, $[5]=5$, $[2.8]=2$, and $[-2.3]=-3$.

The perimeter of a triangle ABC is 48. The point D is the midpoint of AB such that DC=DA=10. Find the area of triangle CBD.