Segments Formed by Secants and Tangents
Segments of Secant Segments and Tangent Segments
Move points A, B, C, and D. Do you see any relationship between the shown segment lengths? Click the Show Triangles check box. Do you see any similar triangles? How could you prove that the triangles are similar? Click the Show Scale Factor check box. What is the scale factor between the similar triangles? Click the Show Segment Products check box. Cross-multiply the scale factor ratios to obtain a relationship between the four segment lengths. What happens to the products when you drag the points A, B, C, and D? What happens if you drag point A to point D or point C to point B, so that your secant becomes a tangent?