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Equilateral triangles ABX and ACY are described on sides AB, AC of a triangle ABC externally to triangle ABC. Prove that CX=BY.

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by mangal

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by mangal

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u can see by cosine law

CX²=BC²+BX^2-2(BC)(BX)cos(60)

CX²=BC²+AB^2-(BC)(AB)...(1)

similarly

BY²=BC²+CY²-2(BC)(CY)cos(60)

BY²=BC²+AC²-(BC)(AC)

as AB=AC

BY²=BC²+AB^2-(BC)(AB)..(2)

(1)=(2)

therefore

BY=CY

thus it is an eqilateral triangle and as per given data abx=acy thus cx =by