Problem
GEO-B2-M02-P003 Intersecting Chords
#3
★★☆☆☆ Level 2 of 5
Chords \(AB\) and \(CD\) of a circle meet at point \(X\). It is known that \(XA=8\), \(XB=6\), \(XC=4\). Find \(XD\).
The products of chord parts are equal.
By the intersecting-chords theorem, \(XA\cdot XB=XC\cdot XD\). Hence \(8\cdot6=4\cdot XD\), so \(XD=12\).
The internal version of power of a point.