The area of the square LMNP is 50 square units
How to determine the area of the square?
The circumference of the circle is given as:
C = 10π
Circumference is calculated as:
C = 2πr
So, we have:
2πr = 10π
Divide by 2π
r = 5
This represents the length OM
The length PM is calculated as:
PM = 2 * OM
This gives
PM = 2 * 5
PM = 10
The length (PN) of the square is then calculated as:
PM = PN√2
This gives
10 = PN√2
Square both sides
100 = PN^2 * 2
Divide by 2
50 = PN^2
Rewrite as:
PN^2 = 50
Hence, the area of the square LMNP is 50 square units
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