WSP Power of a Point

• Power of a Point

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?

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
• Geometry / Measurement
• Functions and Trigonometry
• 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)
• Geometry
• Measurement