Problem:
In parallelogram ABCD, point M is on AB so that ABAM=100017, and point N is on AD so that ADAN=200917. Let P be the point of intersection of AC and MN. Find APAC.
Solution:
Let point S be on AC such that NS is parallel to AB. Because △ASN is similar to △ACD,ACAS=ACAP+PS=ADAN=200917. Because △PSN is similar to △PAM,APPS=AMSN=100017AB200917CD=20091000, and so APPS+1= 20093009. Hence AP200917AC=20093009, and APAC=177.
The problems on this page are the property of the MAA's American Mathematics Competitions
