Problem
GEO-B2-M04-P013 A Trapezoid Base from the Ratio of Diagonals
#13
★★★★☆ Level 4 of 5
In trapezoid \(ABCD\), bases \(AD\) and \(BC\) are parallel, and the diagonals meet at \(O\). It is known that \(AD=21\) and \(AO:OC=3:2\). Find \(BC\).
Use the similarity \(\triangle AOD \sim \triangle COB\).
Since \(AD \parallel BC\), triangles \(AOD\) and \(COB\) are similar. Therefore \(\frac{AD}{BC}=\frac{AO}{OC}=\frac{3}{2}\). Hence \(\frac{21}{BC}=\frac{3}{2}\), so \(BC=14\).
A moderate computational problem because the student must choose the correct triangles.