Problem
GEO-B1-M08-P010 Diagonals of a Trapezoid
#10
★★★☆☆ Level 3 of 5
In trapezoid \(ABCD\), bases \(AD\parallel BC\), \(AD=21\), \(BC=14\). The diagonals meet at point \(O\). Find \(AO:OC\) and \(DO:OB\).
Prove the similarity of \(\triangle AOD\) and \(\triangle COB\).
Triangles \(AOD\) and \(COB\) are similar: the angles at \(O\) are vertical, and the other corresponding angles are equal because \(AD\parallel BC\). Therefore \(AO:OC=DO:OB=AD:BC=21:14=3:2\).
A mixed problem on trapezoids and similarity.