Four distinct points are arranged in a plane so that the segments connecting them have lengths a, a, a, a, 2 a, and b. What is the ratio of b to a ?

**Answer Choices**

A. \sqrt{3}

B. 2

C. \sqrt{5}

D. 3

E. \pi

Four distinct points are arranged in a plane so that the segments connecting them have lengths a, a, a, a, 2 a, and b. What is the ratio of b to a ?

**Answer Choices**

A. \sqrt{3}

B. 2

C. \sqrt{5}

D. 3

E. \pi