In isosceles right triangle ABC, shown here, AC = BC. Point X is on side BC such that CX = 6 and XB = 12, and Y is on side AB such that XY is perpendicular to AB. What is the ratio of BY to YA?
+128408 Note that since BC = AC, then BA = 18sqrt (2)
Note that triangle YBX is similar to triangle CBA
Therefore
BY / BX = CB / BA
BY / 12 = 18 / (18 sqrt (2)
BY /12 = 1/sqrt 2
BY = 12/ sqrt (2) = 6 sqrt (2)
So YA = BA - BY = 18sqrt 2 - 6 sqrt 2 = 12 sqrt 2
So
BY : YA = 6sqrt (2) : 12 sqrt (2) = 1 : 2
