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UKMT Grey Kangaroo, 2016

Geometry Difficulty 2.0 Junior Find the answer United Kingdom

The diagram shows a pentagon. The lengths of the sides of the pentagon are given in the diagram. Sepideh draws five circles with centres $A$ , $B$ , $C$ , $D$ and $E$ such that the two circles with centres at the ends of a side of the pentagon touch on that side. Which point is the centre of the largest circle that she draws?

(A) $A$ (B) $B$ (C) $C$ (D) $D$ (E) $E$

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