The Journal of the Indian Mathematical Society

V. Ramaswami Aiyar

Abstract

Let a straight line MN of length a+b slide between two rectangular lines XOX', YOY', Let it be divided at P into parts MP = a, PN =b. The locus of P, we know, is an ellipse. In y, fact, if the angle MNO = Φ, the co-ordinates of P are a cosΦ, b sinΦ referred to OX, OY as axes, and P describes the ellipse x²/a²+y² b²=1 we shall call E.

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V. Ramaswami Aiyar

Abstract

Let ABC be a given triangle, O its circumcentre and P,P' a pair of isogonal conjugates. We shall use the following notation :

R for the circumradius of ABC ;

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V. Ramaswami Aiyar

Abstract

Now, let T' conicide with T. Then TT' becomes the tangent at T to the circumcirole. Also, since the Simson lines of T, T' are tangents to Steiner's tricusp, their intersection coincides in the limit, with the point of contact of the Simson line of T and the tricusp.

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V. Ramaswami Aiyar

Abstract

General Properties of the Orthopolar Circle

Let ABC be a given triangle and D,E,F the middle points of its sides. Let LL' be any straight line ; and Ap, Bq, Cr perpendiculars drawn thereto from the vertices.

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