De, Prithwijit and Shirali, Shailesh
(2018)
Problems for the senior school.
At Right Angles, 7 (3).
pp. 103105.
ISSN 25821873
Abstract
Let ABC be an equilateral triangle with centre O. A line through C meets the circumcircle of triangle AOB at
points D and E. Prove that the points A, O and the midpoints of segments BD, BE are concyclic.
Three nonzero real numbers are given. It is given that if they are written in any order as the coefficients of a
quadratic trinomial, then each of these trinomials has a real root. Does it follow that each of these trinomials has
a positive root?
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