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AB is a diameter of a circle and C is a point on the circle, distinct from A and B. If AC = 5 cm and BC = 12 cm, what is the radius of the circle?

Competition practiceGeometry
  • A13 cm
  • B8.5 cm
  • C6.5 cm
  • D5 cm

Step-by-Step Solution

An angle in a semicircle is a right angle, so angle ACB = 90°. Then AB = √(25 + 144) = √169 = 13 cm. AB is the diameter, so the radius is 13/2 = 6.5 cm.
Answer: C) 6.5 cm

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