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Soccer Problem

Math Content:

A soccer player is on a breakaway, dribbling the ball downfield, parallel to a sideline. From where should she shoot to have the best chance of making a goal? That is, at what point will the angle formed by the player and the two goal posts be the greatest?

  • Adjust how far player C is from the the goal by dragging Point C along the light blue dotted line.
  • The Show/Hide Circle buttons allow you to create a circle that will help solve the problem.
    • The radius of the circle can be modified by dragging the black point on the slider labeled, radius of circle.
    • Drag the circle around the workspace by its center point.

Drag point C so that the angle is as large as possible along that breakaway line.

    Click Show Circle. Where should the circle be placed, and what should its radius be so that Player C has the best chance of making a goal? What is the relationship between point P and the circle?