Problem 45476. Inscribed circle in a triangle

Created by Asif Newaz

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33 Solutions
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Last Solution submitted on Sep 13, 2021

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William on 9 May 2020

Asif,
I must be misunderstanding this problem. It seems to be that a triangle with x = 20 and y = 30 could not have an area greater than x*y/2 = 300. Yet, problem 1 says the area is 600. How could it be so large? My calculations says that with this x and y, there is no solution for r = 10.

Asif Newaz on 10 May 2020

hello william,
in the triangle ABC, the radius of the circle intersects AB in the point 'c' (small letter c in the figure).
There, Ac=x and Bc=y.

William on 10 May 2020

I see. Then you need to change the statement of the problem to say "Ac = x" and "Bc = y", rather than "AC = x" and "BC = y". Since "C" and "c" are different points on the diagram, this changes the problem completely. As written, the problem is quite difficult to solve.

Asif Newaz on 11 May 2020

yes .. i didn't see that before

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Problem 45476. Inscribed circle in a triangle

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Problem 45476. Inscribed circle in a triangle

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