From the apex of the sector, drop a line that bisects the angle pi/3 to the centre of the circle. That line has length (6-r). Using the fact that a tangent to a circle is at right angles to a radius you can form a right angled triangle whose hypotenuse is (6-r) and it has one other side of r.
Hope that's enough
Hope that's enough
Draw a line from the centre of the white circle to the top of the figure and another again from the centre of the white circle to the point where the circle meets one of the sides. Now the length of the first line must be 6-r (where r is the radius you require) and the length of the second line must be r itself. I hope you recognise you have a right angled triangle. what is the angle at the top of this and what is the sine of that angle????
Original post by mikelbird
Draw a line from the centre of the white circle to the top of the figure and another again from the centre of the white circle to the point where the circle meets one of the sides. Now the length of the first line must be 6-r (where r is the radius you require) and the length of the second line must be r itself. I hope you recognise you have a right angled triangle. what is the angle at the top of this and what is the sine of that angle????
I managed to work out all of the values fine. I just never understood where they got the working from.
I mean I drew the diagram and was able to work out the bottom part was r, the left side was 6-r and the top angle is pi/6. This left the hyp. unknown. From here what am I supposed to use? I tried using sin(pi/6)/r = sin(pi/3) / (6-r) but that got me a value of r which is not 2?!
(edited 10 years ago)
Original post by Henry.Lister
I managed to work out all of the values fine. I just never understood where they got the working from.
I mean I drew the diagram and was able to work out the bottom part was r, the left side was 6-r and the top angle is pi/3. This left the hyp. unknown. From here what am I supposed to use? I tried using sin(pi/6)/r = sin(pi/3) / (6-r) but that got me a value of r which is not 2?!
I mean I drew the diagram and was able to work out the bottom part was r, the left side was 6-r and the top angle is pi/3. This left the hyp. unknown. From here what am I supposed to use? I tried using sin(pi/6)/r = sin(pi/3) / (6-r) but that got me a value of r which is not 2?!
Sin (pi/6) = r/6-r is the next step. You should then get 1/2 = r/6-r. And from then on you should get r = 2.
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