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Practice: The Power of a Point Theorem

The power of the points 𝐴, 𝐵, and 𝐶 with respect to the circle 𝐾 are 𝑃(𝐴)=4, 𝑃(𝐵)=14, and 𝑃(𝐶)=1. The circle 𝐾 has center 𝑀 and a radius of 10 cm. Calculate the distance between 𝑀 and each of the points.

  • A𝐴𝑀=14cm, 𝐵𝑀=24cm, 𝐶𝑀=9cm
  • B𝐴𝑀=14cm, 𝐵𝑀=26cm, 𝐶𝑀=3cm
  • C𝐴𝑀=226cm, 𝐵𝑀=114cm, 𝐶𝑀=311cm
  • D𝐴𝑀=104cm, 𝐵𝑀=114cm, 𝐶𝑀=99cm
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