Math Gold Medalist

Lor

2023 AIME I 

Problem 5

Let $P$ be a point on the circle circumscribing square $ABCD$ that satisfies $PA \cdot PC = 56$ and $PB \cdot PD = 90.$ Find the area of $ABCD.$

Sine Law

Important Trigonometry Formulas

Algorithm to Get Square Root

Use sine law in triangles PBC and PAD.

Then multiply them.

Consider arc AB =2a

Then you can conclude 45.sin(90+a).sin(a) = 28.sin(45-a).sin(135-a)

 

 

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   Solution