Problem
GEO-B2-M02-P007 Ratio of Chord Parts
#7
★★★☆☆ Level 3 of 5
Chords \(AB\) and \(CD\) meet at point \(X\). It is known that \(XA:XB=2:5\), \(XC=6\), \(XD=15\). Find \(XA\) and \(XB\).
Let \(XA=2k\), \(XB=5k\).
Let \(XA=2k\), \(XB=5k\). Then \(XA\cdot XB=10k^2\). By the chord theorem, \(10k^2=XC\cdot XD=6\cdot15=90\). Hence \(k^2=9\), \(k=3\). Therefore \(XA=6\), \(XB=15\).
A problem combining a ratio and a product.