Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-24T13:53:48.995Z Has data issue: false hasContentIssue false

Note on Mr Tweedie's Theorem in Geometry

Published online by Cambridge University Press:  20 January 2009

Rights & Permissions [Opens in a new window]

Extract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let ABC, A′B′C′ (Fig. 4) be two triangles equiangular in the same sense. Let BC, B′C′ meet in X. Describe circles round BXB′, CXC′ to meet again in O. Then it is easy to see that the triangles BOC, COA, AOB are equiangular in the same sense to the triangles B′OC′, C′OA′, A′OB′ respectively. Hence the triangles AOA′, BOB′, COC′ are similar;

a. AA′, b. BB′, c. CC′ are proportional to a. AO, b. BO, c. CO, where a, b, c are the sides of the triangle ABC.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1903