Community post

Arithmetic Progression in a triangle

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Greetings! I am pleased that there are new followers even in the midst of my long break from Steemit. A warm welcome to everybody.

The following question is taken from an old General Certificate in Education Advanced Level Mathematics Examination. It is a national examination taken by Singapore junior college students (equivalent to about grade 12), but the question was from an older syllabus.

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The problem tests you on arithmetic progressions. One important characteristic of an A.P. is that the terms share a common difference. So if x, y and z are consecutive terms of an A.P., then y - x equal to z - y.

In case you don't know, here the standard labelling of a triangle ABC. Capital (upper case) letters are used to label vertices, while lower case letters are used to label the length of their respective opposite sides.

APGP --- 03.png

Although this question involves trigonometry, particularly the Sine Law and the Cosine Law, the solution would be a pain to write down if we stick to trigonometry. I found that the solution is easier to write down if we reduce it to an algebra problem.

My final solution is presented as follows:-

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@tradersharpe
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