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

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August 8, 2020
geometry3D geometryspherecylinder

Problem Statement

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
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