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Question Number 185384 by Mingma last updated on 20/Jan/23

Answered by HeferH last updated on 21/Jan/23

Commented by HeferH last updated on 21/Jan/23

R = ((13 + 2r)/2)  ( ((13+2r)/2) − r)^2 = r^2  + (((13 + 2r)/2) − r −4)^2    r = 6    ⇒ R = ((13+12)/2) = 12.5

$${R}\:=\:\frac{\mathrm{13}\:+\:\mathrm{2}{r}}{\mathrm{2}} \\ $$$$\left(\:\frac{\mathrm{13}+\mathrm{2}{r}}{\mathrm{2}}\:−\:{r}\right)^{\mathrm{2}} =\:{r}^{\mathrm{2}} \:+\:\left(\frac{\mathrm{13}\:+\:\mathrm{2}{r}}{\mathrm{2}}\:−\:{r}\:−\mathrm{4}\right)^{\mathrm{2}} \\ $$$$\:{r}\:=\:\mathrm{6}\: \\ $$$$\:\Rightarrow\:{R}\:=\:\frac{\mathrm{13}+\mathrm{12}}{\mathrm{2}}\:=\:\mathrm{12}.\mathrm{5}\: \\ $$

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