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IOQM 2022-23 P-13

Source:

October 30, 2022
geometrytrig basharithmetic sequenceIOQM

Problem Statement

Let ABCABC be a triangle and let DD be a point on the segment BCBC such that AD=BCAD=BC. \\ Suppose ∠CAD=x∘,∠ABC=y∘\angle{CAD}=x^{\circ}, \angle{ABC}=y^{\circ} and ∠ACB=z∘\angle{ACB}=z^{\circ} and x,y,zx,y,z are in an arithmetic progression in that order where the first term and the common difference are positive integers. Find the largest possible value of ∠ABC\angle{ABC} in degrees.
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