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Question Number 112626 by Aina Samuel Temidayo last updated on 09/Sep/20

Answered by som(math1967) last updated on 09/Sep/20

$$\mathrm{a})\frac{\mathrm{x}-\mathrm{y}}{\mathrm{b}-\mathrm{a}}=\frac{\mathrm{y}-\mathrm{z}}{\mathrm{c}-\mathrm{b}}=\frac{\mathrm{z}-\mathrm{x}}{\mathrm{a}-\mathrm{c}}$$

Commented by Aina Samuel Temidayo last updated on 09/Sep/20

$$\mathrm{Solution}\mathrm{please}?$$

Commented by som(math1967) last updated on 09/Sep/20

$$\mathrm{let}\frac{\mathrm{x}}{\mathrm{b}+\mathrm{c}}=\frac{\mathrm{y}}{\mathrm{c}+\mathrm{a}}=\frac{\mathrm{z}}{\mathrm{a}+\mathrm{b}}=\mathrm{k}$$$$\therefore \mathrm{x}=\mathrm{k}(\mathrm{b}+\mathrm{c})$$$$\mathrm{y}=\mathrm{k}(\mathrm{c}+\mathrm{a})$$$$\mathrm{z}=\mathrm{k}(\mathrm{a}+\mathrm{b})$$$$\therefore \mathrm{x}-\mathrm{y}=\mathrm{k}(\mathrm{b}+\mathrm{c}-\mathrm{c}-\mathrm{a})=\mathrm{k}(\mathrm{b}-\mathrm{a})$$$$\therefore \frac{\mathrm{x}-\mathrm{y}}{\mathrm{b}-\mathrm{a}}=\mathrm{k}$$$$\mathrm{again}\mathrm{y}-\mathrm{z}=\mathrm{k}(\mathrm{c}-\mathrm{b})$$$$\therefore \frac{\mathrm{y}-\mathrm{z}}{\mathrm{c}-\mathrm{b}}=\mathrm{k}$$$$\mathrm{by}\mathrm{same}\mathrm{way}\frac{\mathrm{z}-\mathrm{x}}{\mathrm{a}-\mathrm{c}}=\mathrm{k}$$$$\mathrm{so}\frac{\mathrm{x}-\mathrm{y}}{\mathrm{b}-\mathrm{a}}=\frac{\mathrm{y}-\mathrm{z}}{\mathrm{c}-\mathrm{b}}=\frac{\mathrm{z}-\mathrm{x}}{\mathrm{a}-\mathrm{c}}$$

Commented by Aina Samuel Temidayo last updated on 09/Sep/20

$$\mathrm{Thanks}.$$

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