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circle with diameter BC covers triangle bounded by AK,BL,CM

Source: Indian Postal Coaching 2008 set 2 p2

May 25, 2020
geometrycircleratio

Problem Statement

Let ABCABC be an equilateral triangle, and let K,L,MK, L,M be points respectively on BC,CA,ABBC, CA, AB such that BK/KC=CL/LA=AM/MB=λBK/KC = CL/LA = AM/MB =\lambda . Find all values of λ\lambda such that the circle with BCBC as a diameter completely covers the triangle bounded by the lines AK,BL,CMAK,BL,CM.
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