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Problem 655

AMC 10/12, early questions

Geometry Difficulty 3.0 Find the answer UKMT Pink Kangaroo · United Kingdom · 2022

The lengths of the sides of pentagon $ABCDE$ are as follows: $AB = 16$ cm, $BC = 14$ cm, $CD = 17$ cm, $DE = 13$ cm, $AE = 14$ cm. Five circles with centres at the points $A, B, C, D, E$ are drawn so that each circle touches both of its immediate neighbours. Which point is the centre of the largest circle? (A) $A$ (B) $B$ (C) $C$ (D) $D$ (E) $E$

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