WSP Power of a Point

  • Power of a Point

    Grade: High School

    Use this tool to investigate what happens when point P is moved to various points within, on, and outside the circle. What, if any, relationships can you identify among the segments and radius?

    Activity

    Instructions

    Dragging point G will change the size of the circle, dragging P will move the point of intersection, and dragging Points A, B, C, and D will change the location of the chords.
    The Show Segment Length buttons will show the lengths of: AP, BP, CP, and DP (in cm). The Show Products button displays the value of two products, AP × BP and CP × DP.

    Exploration

    What, if any, relationships can you identify among the segments and radius?

    Objectives and Standards

    NCTM Standards and Expectations
    • Understand that by similarity, side ratios in right triangles are properties of the angles in the triangle, leading to definitions of trigonometric ratios for acute angles.
    • High School (9-12)