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MATH / Let A=(2,0), B=(0,2), C=(−2,0), and D=(0,−2). Compute the greatest possible value of the product PA⋅PB⋅PC⋅PD, where P is a point on the circle x²+y²=9.

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problem

Let A=(2,0)A = (2, 0), B=(0,2)B = (0, 2), C=(−2,0)C = (-2, 0), and D=(0,−2)D = (0, -2). Compute the greatest possible value of the product PA⋅PB⋅PC⋅PDPA \cdot PB \cdot PC \cdot PD, where PP is a point on the circle x2+y2=9x^2 + y^2 = 9.
Plain-text mathematical notation (without MathML)
Let A=(2,0), B=(0,2), C=(−2,0), and D=(0,−2).  Compute the greatest possible value of the product PA⋅PB⋅PC⋅PD, where P is a point on the circle x²+y²=9.
Original LaTeX notation
Let $A = (2, 0)$, $B = (0, 2)$, $C = (-2, 0)$, and $D = (0, -2)$.  Compute the greatest possible value of the product $PA \cdot PB \cdot PC \cdot PD$, where $P$ is a point on the circle $x^2 + y^2 = 9$.

level

Level 4

type

Precalculus

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Source and history

task_id
35e98d43-4ed2-523c-bf27-4db17ee80770
task_key
precalculus--test--35e98d43-4ed2-523c-bf27-4db17ee80770
task_revision_id
1
config / split
precalculus / test

Official source

initial import