Circles

[Merida]

Denote the legs of a right triangle as a and b . Let the radius of the circumscribed circle be R and the radius of the inscribed circle be r
Find (a + b)/(r+R)

 

[Dr.Peterson]

Denote the legs of a right triangle as a and b . Let the radius of the circumscribed circle be R and the radius of the inscribed circle be r
Find (a + b)/(r+R)View attachment 23293

I presume you're asking us to check your work.

You started with a false assumption, that the incircle is tangent to the hypotenuse at the circumcenter O. It is not, in general:


Your answer of 2 may still be right, since your work does apply to the right isosceles triangle; but you have not shown that it is always 2.

 

[Merida]

I presume you're asking us to check your work.

You started with a false assumption, that the incircle is tangent to the hypotenuse at the circumcenter O. It is not, in general:
View attachment 23302

Your answer of 2 may still be right, since your work does apply to the right isosceles triangle; but you have not shown that it is always 2.

Ok , so the question hasn’t mentioned the triangle is isoceless , so .. that would mean 2 is wrong . And if that’s the case is it possible to find out the value asked for in the question without the assumption of it being isosceles

 

[Dr.Peterson]

Yes, it can still be done.

Find the lengths of AE and CF, and use the fact that they are equal to AD and CD respectively ...