# Problems for the senior school

De, Prithwijit and Shirali, Shailesh (2018) Problems for the senior school. At Right Angles, 7 (2). pp. 123-125. ISSN 2582-1873

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## Abstract

Problem VII-2-S.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 VII-2-S.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 VII-2-S.3 Three non-zero 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]

Item Type: Articles in APF Magazines
Authors: De, Prithwijit and Shirali, Shailesh
Document Language:
Language
English
Uncontrolled Keywords: Tournament of the towns, coin problems
Subjects: Natural Sciences > Mathematics
Divisions: Azim Premji University > University Publications > At Right Angles
Full Text Status: Public
URI: http://publications.azimpremjifoundation.org/id/eprint/1597
Publisher URL: http://apfstatic.s3.ap-south-1.amazonaws.com/s3fs-...