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Question Number 161866 by Tawa11 last updated on 23/Dec/21

Commented by mr W last updated on 23/Dec/21

$$\frac{BC}{10}=\frac{6}{6+9}\Rightarrow BC=4$$$$\frac{AC}{6}=\frac{7.5}{9}\Rightarrow AC=5$$$$\frac{AX}{6}=\frac{5-AX}{4}\Rightarrow AX=3\Rightarrow XC=5-3=2$$

Commented by Tawa11 last updated on 23/Dec/21

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}.\mathrm{I}\mathrm{understand}\mathrm{now}.$$

Commented by mr W last updated on 23/Dec/21

$${it}^{\prime }sfinewhenyouunderstandnow.$$

Answered by som(math1967) last updated on 23/Dec/21

$$\frac{AB}{AD}=\frac{BC}{DE}[BC\parallel DE\therefore △ABC\sim △ADE]$$$$\frac{6}{15}=\frac{BC}{10}\Rightarrow BC=4cm$$$$againBC\parallel DE$$$$\therefore \frac{AB}{BD}=\frac{AC}{CE}$$$$\frac{6}{9}=\frac{AC}{7.5}\Rightarrow AC=5cm$$$$BXisbisectorof\mathrm{\angle }ABC$$$$\therefore \frac{AX}{XC}=\frac{AB}{BC}=\frac{6}{4}=\frac{3}{2}$$$$\therefore AX:XC=3:2$$$$AC=5cm$$$$\therefore AX=\frac{3}{5}\times 5=3cmans$$$$XC=\frac{2}{5}\times 5=2cmans$$$$$$

Commented by Tawa11 last updated on 23/Dec/21

$$\mathrm{God}\mathrm{bless}\mathrm{you}\mathrm{sir}$$

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