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Question Number 5529 by Rasheed Soomro last updated on 18/May/16

Commented by Rasheed Soomro last updated on 18/May/16

$$△\mathrm{ABC}\mathrm{is}\mathrm{an}\mathrm{equilaterl}\mathrm{triangle}.$$$$\mathrm{D},\mathrm{E},\mathrm{F}\mathrm{are}\mathrm{mid}-\mathrm{points}\mathrm{of}\mathrm{the}\mathrm{sides}.$$$$\mathrm{The}\mathrm{centres}\mathrm{of}\mathrm{arcs}\mathrm{are}\mathrm{vertices}\mathrm{of}$$$$△\mathrm{ABC}.$$$$\left(a\right)\mathrm{AB}=\mathrm{x},\mathrm{GH}=?$$$$\left(b\right)△\mathrm{ABC}\mathrm{is}\mathrm{equilateral},\mathrm{prove}\mathrm{that}$$$$△\mathrm{GHI}\mathrm{is}\mathrm{also}\mathrm{equilateral}.$$$$$$

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