Home > A Level, Maths > A little circle problem 

A little circle problem 

I’ve just seen this post from Colin Beveridge  (@icecolbeveridge) answering this question:

Naturally I had a go at it before reading Colin’s solution. When I read his I found a lovely concise solution that we slightly different to mine, so I thought I’d share mine.

I started by just drawing a right angled triangle from the centre of the circle like so.

I seem to have cut off the denominator of 6 on the angle there. I know that the hypotenuse is 12-r (where r is radius) and the side opposite the known angle is r.

This means I can use the sine ratio of pi/6 to get  

r/(12-r)  = 1/2

Which leads to:

2r = 12 – r

Then 

3r = 12

r = 4

Which is the same as Colin got. 

I’ve seen questions like this on A level papers before and I know they often throw students, so I make sure I explore lots of geometry based problems and puzzles to combat this. I’d be interested to know which way you would approach this. Colin and I used a very similar approach, just differing in the point at which we introduced the 12. Which way did you do it? 

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Categories: A Level, Maths Tags: , , ,
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