MathDB

2022 Team P4

Source:

February 28, 2022

team

Problem Statement

Let

\triangle ABC

be equilateral with integer side length. Point

X

lies on

\overline{BC}

strictly between

B

and

C

such that

BX<CX

. Let

C'

denote the reflection of

C

over the midpoint of

\overline{AX}

. If

BC'=30

, find the sum of all possible side lengths of

\triangle ABC

.
Proposed by Connor Gordon

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