Mathematics

Mathematics

Problem

10. CD and GH are respectively the bisectors of

\angle \mathrm{ACB}

and

\angle \mathrm{EGF}

such that D and H lie on sides AB and FE of

\triangle \mathrm{ABC}

and

\triangle \mathrm{EFG}

respectively. If

\triangle \mathrm{ABC} \sim \triangle \mathrm{FEG}

, show that: (i)

\frac{\mathrm{CD}}{\mathrm{GH}}=\frac{\mathrm{AC}}{\mathrm{FG}}

(ii)

\triangle \mathrm{DCB} \sim \triangle \mathrm{HGE}

(iii)

\triangle \mathrm{DCA} \sim \triangle \mathrm{HGF}

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