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?
What is the ratio of BY to YA?
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\(BY:YA=\frac{12}{\sqrt{2}}:(18\cdot \sqrt{2}-\frac{12}{\sqrt{2}})\\ BY:YA=12:(18\cdot 2-12)=12:24\\ \color{blue}BY:YA=1:2 \)
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