To construct tangents from a point outside a circle:

  1. Join the external point to the center of the circle.
  2. Construct the perpendicular bisector of this line segment.
  3. The bisector intersects the segment at the center of a new circle, which intersects the original circle at tangency points.
  4. Join these points to the external point to get the tangents.

This simulation lets you click any external point. It draws two tangents and marks key points: center, external point, and tangency points.

Click anywhere outside the circle to draw tangents.

Center: O | External Point: P | Tangent Points: A, B

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