Circles - Theorems and Properties - Coordinate Geometry Applications - Case Studies

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Q. If two circles have radii of 3 units and 4 units, what is the distance between their centers if they are externally tangent?
  • A. 1 unit
  • B. 7 units
  • C. 12 units
  • D. 5 units
Q. In a coordinate plane, what is the midpoint of the line segment connecting the points (1, 2) and (3, 4)?
  • A. (2, 3)
  • B. (1, 2)
  • C. (3, 4)
  • D. (4, 6)
Q. In a triangle, if two sides are 7 units and 24 units, what is the maximum possible length of the third side?
  • A. 30 units
  • B. 25 units
  • C. 31 units
  • D. 32 units
Q. What is the length of the arc of a circle with a radius of 10 units that subtends an angle of 60 degrees at the center?
  • A. 10π/3 units
  • B. 5π units
  • C. 10π/6 units
  • D. 20π/3 units
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