How to calculate the radius of a right triangle, having the sum of the two inradios of rectangular triangles inscribed in the greater right triangle?

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Calculate the radius of the right triangle ABC, that is to say 'I'



If R + r = 20.



enter image description here



The three rectangular triangles are similar. The inradio of a right triangle has met its legs and its hypotenuse. To equal everything to r, i can put R = 20-r




geometry euclidean-geometry triangle circle tangent-line




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  • Puede usted escribir en Inglés?
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    Aug 1 at 1:40










  • It is English...
    – Strong
    Aug 1 at 1:42










  • K thanks but the picture is now missing.
    – Mohammad Zuhair Khan
    Aug 1 at 1:45










  • It is done.....
    – Strong
    Aug 1 at 1:49










  • Please invent a better name than rectangular triangle.
    – DanielWainfleet
    Aug 1 at 6:24














up vote
1
down vote

favorite












Calculate the radius of the right triangle ABC, that is to say 'I'



If R + r = 20.



enter image description here



The three rectangular triangles are similar. The inradio of a right triangle has met its legs and its hypotenuse. To equal everything to r, i can put R = 20-r




geometry euclidean-geometry triangle circle tangent-line




share|cite|improve this question





















  • Puede usted escribir en Inglés?
    – Mohammad Zuhair Khan
    Aug 1 at 1:40










  • It is English...
    – Strong
    Aug 1 at 1:42










  • K thanks but the picture is now missing.
    – Mohammad Zuhair Khan
    Aug 1 at 1:45










  • It is done.....
    – Strong
    Aug 1 at 1:49










  • Please invent a better name than rectangular triangle.
    – DanielWainfleet
    Aug 1 at 6:24












up vote
1
down vote

favorite









up vote
1
down vote

favorite











Calculate the radius of the right triangle ABC, that is to say 'I'



If R + r = 20.



enter image description here



The three rectangular triangles are similar. The inradio of a right triangle has met its legs and its hypotenuse. To equal everything to r, i can put R = 20-r




geometry euclidean-geometry triangle circle tangent-line




share|cite|improve this question













Calculate the radius of the right triangle ABC, that is to say 'I'



If R + r = 20.



enter image description here



The three rectangular triangles are similar. The inradio of a right triangle has met its legs and its hypotenuse. To equal everything to r, i can put R = 20-r





geometry euclidean-geometry triangle circle tangent-line





share|cite|improve this question












share|cite|improve this question




share|cite|improve this question








edited Aug 1 at 4:18









Michael Rozenberg

87.4k1577179




87.4k1577179









asked Aug 1 at 1:25









Strong

246




246











  • Puede usted escribir en Inglés?
    – Mohammad Zuhair Khan
    Aug 1 at 1:40










  • It is English...
    – Strong
    Aug 1 at 1:42










  • K thanks but the picture is now missing.
    – Mohammad Zuhair Khan
    Aug 1 at 1:45










  • It is done.....
    – Strong
    Aug 1 at 1:49










  • Please invent a better name than rectangular triangle.
    – DanielWainfleet
    Aug 1 at 6:24
















  • Puede usted escribir en Inglés?
    – Mohammad Zuhair Khan
    Aug 1 at 1:40










  • It is English...
    – Strong
    Aug 1 at 1:42










  • K thanks but the picture is now missing.
    – Mohammad Zuhair Khan
    Aug 1 at 1:45










  • It is done.....
    – Strong
    Aug 1 at 1:49










  • Please invent a better name than rectangular triangle.
    – DanielWainfleet
    Aug 1 at 6:24















Puede usted escribir en Inglés?
– Mohammad Zuhair Khan
Aug 1 at 1:40




Puede usted escribir en Inglés?
– Mohammad Zuhair Khan
Aug 1 at 1:40












It is English...
– Strong
Aug 1 at 1:42




It is English...
– Strong
Aug 1 at 1:42












K thanks but the picture is now missing.
– Mohammad Zuhair Khan
Aug 1 at 1:45




K thanks but the picture is now missing.
– Mohammad Zuhair Khan
Aug 1 at 1:45












It is done.....
– Strong
Aug 1 at 1:49




It is done.....
– Strong
Aug 1 at 1:49












Please invent a better name than rectangular triangle.
– DanielWainfleet
Aug 1 at 6:24




Please invent a better name than rectangular triangle.
– DanielWainfleet
Aug 1 at 6:24










1 Answer
1






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$$20=R+r=fracAD+DF-AF2+fracFE+EC-FC2=fracAB+BC-AC2=l$$






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    Can't get much better than that!
    – quasi
    Aug 1 at 4:54










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1 Answer
1






active

oldest

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1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
1
down vote













$$20=R+r=fracAD+DF-AF2+fracFE+EC-FC2=fracAB+BC-AC2=l$$






share|cite|improve this answer

















  • 1




    Can't get much better than that!
    – quasi
    Aug 1 at 4:54














up vote
1
down vote













$$20=R+r=fracAD+DF-AF2+fracFE+EC-FC2=fracAB+BC-AC2=l$$






share|cite|improve this answer

















  • 1




    Can't get much better than that!
    – quasi
    Aug 1 at 4:54












up vote
1
down vote










up vote
1
down vote









$$20=R+r=fracAD+DF-AF2+fracFE+EC-FC2=fracAB+BC-AC2=l$$






share|cite|improve this answer













$$20=R+r=fracAD+DF-AF2+fracFE+EC-FC2=fracAB+BC-AC2=l$$







share|cite|improve this answer













share|cite|improve this answer



share|cite|improve this answer











answered Aug 1 at 4:16









Michael Rozenberg

87.4k1577179




87.4k1577179







  • 1




    Can't get much better than that!
    – quasi
    Aug 1 at 4:54












  • 1




    Can't get much better than that!
    – quasi
    Aug 1 at 4:54







1




1




Can't get much better than that!
– quasi
Aug 1 at 4:54




Can't get much better than that!
– quasi
Aug 1 at 4:54












 

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