A triangle ABC with AC = 20 is inscribed in circle \\omega. A tangent to \\omega is drawn through B. The distance of from A is 25 and that from C is 16. If S denotes the area of the triangle ABC, find the largest integer not exceeding S/20.
Hint 1: Start by analyzing the initial conditions and setting up the basic equations. sin A => 2 32R.
Hint 2: Look for algebraic properties, symmetry, or geometric theorems to simplify. Similarly, c2 = 50R.
Hint 3: Proceed with the final algebraic steps to solve the system. So, ac solve for the final valueR.
Step 1: sin A => 2 32R
Step 2: Similarly, c2 = 50R
Step 3: So, ac = 40R
Step 4: Now, abc 800R 800
Step 5: => S = 200
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