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(342) 4

Part of 1992 Tournament Of Towns

Problems(1)

<A > <C, <D > < B => BC> AD/2

Source: TOT 342 1992 Autumn O J4 S4 - Tournament of Towns

6/10/2024
(a) In triangle ABCABC, angle AA is greater than angle BB. Prove that the length of side BCBC is greater than half the length of side ABAB.
(b) In the convex quadrilateral ABCDABCD, the angle at AA is greater than the angle at CC and the angle at DD is greater than the angle at BB. Prove that the length of side BCBC is greater than half of the length of side ADAD.
(F Nazarov)
geometrygeometric inequalityangles