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The Circles associated with the Triangle, viewed from their Centres of Similitude
Published online by Cambridge University Press: 20 January 2009
Abstract
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The notation adopted in this paper for the triangle ABC is:
G the centroid.
I the centre of the inscribed circle.
I1, I2, I3 the centres of the escribed circles within angles A, B, C.
O the centre of the circumscribed circle.
D, E, F; D1, E1, Fl; D2, E2, F2; D3, E3, F3 the points of contact of the inscribed and escribed circles with BC, CA, AB. The Ds lie all on BC, the Es on CA, and the Fs on AB.
H, K, L the mid points of BC, CA, AB.
X, Y, Z the feet of the perpendiculars from A, B, C, on BC, CA, AB.
A′, B′, C′ the vertices, opposite to A, B, C, of the triangle formed by drawing through A, B, C parallels to BC, CA, AB.
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- Research Article
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- Copyright
- Copyright © Edinburgh Mathematical Society 1883
References
* Two words are wanted to denote I′ and I1′ with respect to ▵ABC.
* These three triads of points are all different, though denoted by the same letters.
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