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R-r-5-2-a-b-c-3-4-5-prove-R-r-radius-h-a-h-b-h-c-1-a-1-b-1-c-bc-ac-ab-prove-




Question Number 147606 by vvvv last updated on 22/Jul/21
(R/r)=(5/2)  ⇒ a:b:c=3:4:5  prove    R,r− radius  h_a :h_b :h_c =(1/a):(1/b):(1/c)=bc:ac:ab  prove
$$\frac{\boldsymbol{\mathrm{R}}}{\boldsymbol{{r}}}=\frac{\mathrm{5}}{\mathrm{2}}\:\:\Rightarrow\:\boldsymbol{{a}}:\boldsymbol{{b}}:\boldsymbol{{c}}=\mathrm{3}:\mathrm{4}:\mathrm{5} \\ $$$$\boldsymbol{\mathrm{prove}}\:\: \\ $$$$\boldsymbol{\mathrm{R}},\boldsymbol{{r}}−\:\boldsymbol{\mathrm{radius}} \\ $$$$\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{a}}} :\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{b}}} :\boldsymbol{\mathrm{h}}_{\boldsymbol{\mathrm{c}}} =\frac{\mathrm{1}}{\boldsymbol{{a}}}:\frac{\mathrm{1}}{\boldsymbol{{b}}}:\frac{\mathrm{1}}{\boldsymbol{{c}}}=\boldsymbol{{bc}}:\boldsymbol{{ac}}:\boldsymbol{{ab}} \\ $$$$\boldsymbol{{prove}} \\ $$

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