Back to Mathematical Olympiad
Difficulty: 3/102022 IOQM 2022 (Q1)

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.

Guide / Hint

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.

Solution

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

Ready to track your progress and master these topics?

Create a free account