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

20Tangent-radius right triangle

PT is tangent to a circle with centre O at T. The radius is 5 cm and PT = 12 cm. Find OP.

OP = 13 cm. Since PT is tangent at T, OT ⊥ PT, so triangle OTP is right-angled at T. By Pythagoras, OP² = 5² + 12² = 169, so OP = 13 cm.

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