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Question Number 195322 by Rupesh123 last updated on 30/Jul/23

Answered by HeferH last updated on 31/Jul/23

say k is the incenter length   k = (A/s)   s = ((AB+AC+BC)/2)   A = ((3k∙BC)/2)   1 = ((3BC)/(AB+AC+BC))   AB+AC= 2BC    ((AB+AC)/(BC)) = 2

$${say}\:{k}\:{is}\:{the}\:{incenter}\:{length} \\ $$$$\:{k}\:=\:\frac{{A}}{{s}} \\ $$$$\:{s}\:=\:\frac{{AB}+{AC}+{BC}}{\mathrm{2}} \\ $$$$\:{A}\:=\:\frac{\mathrm{3}{k}\centerdot{BC}}{\mathrm{2}} \\ $$$$\:\mathrm{1}\:=\:\frac{\mathrm{3}{BC}}{{AB}+{AC}+{BC}} \\ $$$$\:{AB}+{AC}=\:\mathrm{2}{BC} \\ $$$$\:\:\frac{{AB}+{AC}}{{BC}}\:=\:\mathrm{2} \\ $$

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