HMMT November 2017 U26

Points $A, B, C, D$ lie on a circle in that order such that $\frac{A B}{B C}=\frac{D A}{C D}$ . If $A C=3$ and $B D=B C=4$ , find $A D$ .

Dataset text NuminaMath olympiads. Quoted with source.

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\frac{3}{2}

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