Problem
GEO-B2-M02-P001 The Second Secant
#1
★★☆☆☆ Level 2 of 5
From point \(P\) outside a circle, two secants \(PAB\) and \(PCD\) are drawn, where \(A\) and \(C\) are the nearer points of the circle. If \(PA=5\), \(PB=18\), \(PC=6\), find \(PD\).
Write \(PA\cdot PB=PC\cdot PD\).
By the two-secant theorem, \(5\cdot18=6\cdot PD\). Hence \(PD=15\).
Checks that the student uses the whole secant, not only the inner part.