Secants and the tangent
From a point P outside a circle two secants, or a secant and a tangent, are drawn. The products of the segments agree: PA · PB = PC · PD and PT² = PA · PB.
- Russia: grade 9
Guide
A secant is a line meeting the circle in two points. From P outside, a secant meets the circle at A and B (A nearer to P). PA is the outer part and PB the whole secant.
For two secants PA·PB = PC·PD. For a tangent PT and a secant PAB, PT2 = PA·PB.
Drag P and watch the numbers. In the last two tasks you find the numbers yourself.