# The Right Brothers

Geometry Level 3

$$ABC$$ is an isosceles triangle with $$AB = AC$$ and $$BC = 60$$. $$D$$ is a point on $$BC$$ such that the perpendicular distances from $$D$$ to $$AB$$ and $$AC$$ are $$16$$ and $$32$$, respectively. What is the length of $$AB$$?

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