silemus.
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  1. 4No solution, linear system
  2. 5Infinite solutions, linear system
  3. 15Probability from a table
  4. 18Median from a frequency table
  5. 22One solution, discriminant=0
  6. 23Max height of a parabola
  7. 25Exponential decay, 15% off
  8. 29Composing f and g
  9. 32Radius from two points
  10. 33Arc length from central angle
  11. 37Similar triangles ratio
  12. 47Two-ticket system of equations
  13. 51No solution, linear equation
  14. 52Taxi cost inequality
  15. 55Scaling 9x-6y+5
  16. 56Costly text message inequality
  17. 59Solving a square root equation
  18. 62Factor theorem on a cubic
  19. 64Percent growth per year
  20. 66x²+y² from sum and product
  21. 67Sum of roots of intersection
  22. 70Completing the square
  23. 73Percent off, then tax
  24. 74Mean with a score removed
  25. 75Overlapping sets, neither
  26. 81Percent of a percent
  27. 82Average speed, unequal times
  28. 85Fraction of a subgroup
  29. 86Mixing to a target percent
  30. 92Inscribed angle theorem
  31. 93Circle from diameter endpoints
  32. 96Sine-cosine complementary angles
  33. 97Area ratio of similar triangles
  34. 98Diagonal of a rectangle
  35. 100Right triangle, tan from cos
  36. 101Volume displaced raises water

93Circle from diameter endpoints

In the xy\displaystyle xy-plane, the points (−1,3)\displaystyle (-1, 3) and (7,9)\displaystyle (7, 9) are the endpoints of a diameter of a circle. The equation of the circle is (x−h)2+(y−k)2=r2\displaystyle (x - h)^2 + (y - k)^2 = r^2. What is the value of r2\displaystyle r^2?

r² = 25. The center is the midpoint of (−1,3) and (7,9), which is (3,6), and r² is the squared distance from that center to either endpoint: 4² + 3² = 25, confirmed using the other endpoint too.

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