silemus.
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  1. 1Angles in a triangle
  2. 2Exterior angle of a triangle
  3. 3Triangle angle sum
  4. 4Pythagorean theorem
  5. 5Pythagorean theorem
  6. 6Ladder, Pythagorean theorem
  7. 7Diagonal of a rectangle
  8. 8Similar triangles ratio
  9. 9Similar triangles, shadows
  10. 10Similar triangles, area ratio
  11. 11Right triangle, Pythagoras
  12. 1230-60-90 triangle sides
  13. 13Right triangle, find a leg
  14. 14Angle of elevation, right triangle
  15. 15Right triangle trig, finding angle A
  16. 16Arc length of a circle
  17. 17Area of a sector
  18. 18Inscribed angle theorem
  19. 19Angle in a semicircle
  20. 20Tangent-radius right triangle
  21. 21Equal tangent lengths
  22. 22Chord distance from centre
  23. 23Corresponding angles equal
  24. 24Co-interior angles sum to 180
  25. 25Vertical angles equation
  26. 26Interior angles of an octagon
  27. 27Regular polygon from angle
  28. 28Exterior angles of a pentagon
  29. 29Area of a trapezoid
  30. 30Area and side of a rhombus
  31. 31Prism volume and surface area
  32. 32Volume of a cylinder
  33. 33Volume and slant height of cone
  34. 34Volume of a sphere
  35. 35Surface area of a sphere
  36. 36Distance between two points
  37. 37Midpoint of a segment
  38. 38Finding an endpoint from midpoint
  39. 39Line through two points
  40. 40Perpendicular bisector
  41. 41Area of triangle by coords
  42. 42Circle, completing the square

21Equal tangent lengths

From an external point P, two tangents touch a circle at A and B. PA = 3x + 2 and PB = 5x − 8. Find x and the length PA.

Since tangents from the same external point P are equal, PA = PB gives 3x+2 = 5x−8, so x = 5, and PA = 3(5)+2 = 17. Check: PB = 5(5)−8 = 17 ✓, matching PA.

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