My teacher didn't get back to me and I had no sudden moment of enlightenment so I thought I would just have to cope with my frustrations. Then today I just thought I would check and see if anyone has started a thread yet and they had! With model answers! Totally perfect!! But I didn't let myself look at any other answers, that would just frustrate me I think! Here is their solution to the question I got stuck on:
So basically the theorem is that a tangent is perpendicular to the radius of the circle (which I knew!!) which creates a right angled triangle with an angle that is half the angle at the centre of the sector. The height (Hypotenuse) is the radius of the sector (in this case 6) minus the radius that we are trying to calculate. Using sine and a bit of rearrangement you get an answer!
Ironically, as a last resort strategy in the exam I said that the radius was a third of the radius of the sector, I wonder if it is just a coincidence that this also gives you a value of 2 or it actually works every time? I wouldn't get method marks though..
Ironically, as a last resort strategy in the exam I said that the radius was a third of the radius of the sector, I wonder if it is just a coincidence that this also gives you a value of 2 or it actually works every time? I wouldn't get method marks though..
So I suppose it was quite simple in the end... I'm so happy just to know now!
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