2006.10

Part of Ukraine Correspondence MO - geometry

Problems(1)

sum of inradius + radius of mixtiinear excircle is fixed, start with isosceles

Source: 2006 All-Ukrainian Correspondence MO of magazine ''In the World of Mathematics'', grades 5-11 p10

ABC

be an isosceles triangle (

AB=AC

). An arbitrary point

M

is chosen on the extension of the

BC

B

. Prove that the sum of the radius of the circle inscribed in the triangle

AM​​B

and the radius of the circle tangent to the side

AC

and the extensions of the sides

AM, CM

of the triangle

AMC

does not depend on the choice of point

M

geometrymixtilinear excircleradiiifixedisoscelesUkraine Correspondence