2007 Indonesia MO Problems/Problem 1
Let be a triangle with . Let point on side such that is the altitude, point on side such that , and point is the intersection of and . Prove that .
By using the Angle Addition Postulate and substitution, Since is a 30-60-90 triangle, .
Additionally, because is the foot of the altitude from , . Furthermore, by the Base Angle Converse, we must have because . Therefore, by AAS Similarity, , so . Thus, .
Therefore, by substitution, .
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