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Pentagon Problem

Geometry Level 3

In regular pentagon $ABCDE,$ point $M$ is the midpoint of side $AE.$

If line segments $AC$ and $BM$ intersect at point $Z$ and $ZA=3,$ what is the length of $AB?$

3\sqrt{5}

2 \sqrt{5}

4

3

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by Lohith Tummala

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