De, Prithwijit and Shirali, Shailesh
(2018)
Problems for the
senior school.
At Right Angles, 7 (2).
pp. 123125.
Abstract
Problem VII2S.1 Let AB be a fixed line segment in the plane. Let O and P be two points in the plane and on the same side of AB. If ∡AOB = 2 ∡APB, does it necessarily follow that P lies on the circle with centre O and passing through A and B?
Problem VII2S.2 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. [Tournament of Towns]
Problem VII2S.3 Three nonzero real numbers are given. If they are written in any order as 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? [Tournament of Towns]
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