Comments on: Sunday Times Teaser 2572 – Abominable
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Just another WordPress siteThu, 05 May 2016 14:56:38 +0000
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By: Brian Gladman
https://brg.a2hosted.com/?page_id=3461#comment-534
Thu, 05 May 2016 14:56:38 +0000http://ccgi.gladman.plus.com/wp/?page_id=3461#comment-534 The diagram above shows half the layout involved in this teaser. The radii of the circles involved are \(r\), \(3r\), \(4r\) and \(s\). Since the angle \(alpha\) is common to triangles ABD and ACD, we can apply the cosine rule for this angle in both triangles to give: \[(r+s)^2+9r^2-6r(r+s)cosalpha = (4r-s)^2\] \[(r+s)^2+16r^2-8r(r+s)cosalpha=(3r+s)^2\] we can now eliminate the (cosalpha) term and simplify the result to give: \[4r(13s-12r)=0\] Substituting \(s=r-1\) now gives: \[4r(r-13)=0\] giving the radius of the circle for the head as 13 centimetres.
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