Mathematics

Mathematics

Problem

Two radar stations are located at coordinates A(0,0)A(0, 0) and B(24,10)B(24, 10) (distances in kilometers). The coverage area of station AA is a circle with a radius of 13 km13\,\text{km}. The coverage area of station BB is a circle with radius rr. If the boundaries of the two coverage areas intersect orthogonally, calculate the radius rr of station BB 's coverage.

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