# 2016 AMC 12B Problem 21

Geometry Level 4

Let $$ABCD$$ be a unit square. Let $$Q_1$$ be the midpoint of $$\overline{CD}$$. For $$i=1,2,\ldots,$$ let $$P_i$$ be the intersection of $$\overline{AQ_i}$$ and $$\overline{BD}$$, and let $$Q_{i+1}$$ be the foot of the perpendicular from $$P_i$$ to $$\overline{CD}$$.

What is $$\sum\limits_{i=1}^{\infty} \text{Area of }\triangle DQ_iP_i$$?

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