How to Construct the Tangent Line to a Circle

Опубликовал Admin
12-06-2017, 00:20
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A line tangent to a circle touches the circle at exactly one point. The tangent line is perpendicular to the radius of the circle. In maths problems, one can encounter either of two options: constructing the tangent from a point outside of the circle, or constructing the tangent to a circle at a point on the circle.

Constructing a Tangent Line from a Point Outside of the Circle

  1. Setup of the problem. Construct a line, tangent to the circle, passing through point P{\displaystyle P}.
  2. Connect the point P{\displaystyle P} with the centre of the circle. You must first find the centre of the circle if it has not been given to you.
  3. Bisect OP{\displaystyle OP}. The bisector intersects OP{\displaystyle OP} in A{\displaystyle A}.
  4. Construct a circle with radius AP{\displaystyle AP}, centred at A{\displaystyle A}. This circle intersects the original circle at points B{\displaystyle B} and C{\displaystyle C}.
  5. Connect P{\displaystyle P} with B{\displaystyle B} or C{\displaystyle C}. Both PB{\displaystyle PB} an PC{\displaystyle PC} are tangent to the circle.
  6. Erase any construction lines, if needed.

Constructing a Tangent Line to a Circle at a Point on the Circle

  1. Setup of the problem. Construct a line, tangent to the circle at P{\displaystyle P}.
  2. Draw the radius MP{\displaystyle MP}. You must first find the centre of the circle if it has not been given to you.
  3. Extend the radius past the circle.
  4. Construct the perpendicular to the radius through point P{\displaystyle P}. That perpendicular is the tangent to the circle at point P{\displaystyle P}.
  5. Erase any construction lines, if needed.

Things You'll Need

  • Paper
  • Compass
  • Ruler
  • Pencil and/or pen
  • Eraser
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