MathDB

1

Part of 2019 Flanders Math Olympiad

Problems(1)

\sqrt{d}=\sqrt{a}+\sqrt{b}, tangent balls in cylinder (2019 VWO Flanders MO p1)

Source:

8/8/2020
Two touching balls with radii aa and bb are enclosed in a cylindrical tin of diameter dd . Both balls hit the top surface and the shell of the cylinder. The largest ball also hits the bottom surface. Show that d=a+b\sqrt{d} =\sqrt{a} +\sqrt{b} https://1.bp.blogspot.com/-O4B3P3bghFs/Xy1fDv9zGkI/AAAAAAAAMSQ/ePLVnsXsRi0mz3SWBpIzfGdsizWoLmGVACLcBGAsYHQ/s0/flanders%2B2019%2Bp1.png
geometry3D geometryspherecylinder