# Maths - Circle TheoremsWatch

Thread starter 7 years ago
#1
Hello,
I have my exam tomorrow and was stuck on these questions:

1) Calculate the length of AB.
Answer:10.6cm
I tried working out the area of a trapezium somehow but didn't get anywhere

2) A bridge is built in the shape of the arc of a circle, centre O. The width, AB, is 12m and the height is 4m. Calculate the distance AO.
Answer: 6.5m
I tried working out the arc length (didn't know what else to do) and was completely confused from there.

Please help if you can, thank you xx

EDIT: Now finished my exam, thanks for your help everyone xx
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7 years ago
#2
1) the distance between the two centres is 11, and you can form a right angled triangle (3 from the 7, the line between the two centres and from the centre of the smaller circle to 3 down from the other centre), then 11 x sin(3/11) ?

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7 years ago
#3
You need to be thinking about Pythagoras theorem. Make your unknown x and just work it out.
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7 years ago
#4
(Original post by acomber)
You need to be thinking about Pythagoras theorem. Make your unknown x and just work it out.
The square root of 11^2 - 3^2 is 10.6 to 1 dp.

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7 years ago
#5
(Original post by mattparker)
The square root of 11^2 - 3^2 is 10.6 to 1 dp.

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Yes.

you know the distance between the centres of the circles is 7+4=11

Call the height of the triangle 7-4 = 3cm

the unknown is then the other side, x

x = 10.583
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7 years ago
#6
Are you sure about the answer to the second one. I keep ending with 8.48(to 2 decimal place)

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7 years ago
#7
(Original post by zohaib029)
Are you sure about the answer to the second one. I keep ending with 8.48(to 2 decimal place)

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I make it 6.5.

Post your working that leads to the solution 8.48.
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Thread starter 7 years ago
#8
(Original post by zohaib029)
Are you sure about the answer to the second one. I keep ending with 8.48(to 2 decimal place)

Samsung > Apple
(Original post by mattparker)
The square root of 11^2 - 3^2 is 10.6 to 1 dp.

This was posted from The Student Room's iPhone/iPad App

(Original post by acomber)
Yes.

you know the distance between the centres of the circles is 7+4=11

Call the height of the triangle 7-4 = 3cm

the unknown is then the other side, x

x = 10.583

(Original post by notnek)
I make it 6.5.

Post your working that leads to the solution 8.48.
Thank you everyone for your help xx
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7 years ago
#9
(Original post by SM!)
Thank you everyone for your help xx
I assume you managed to do the second one then?

Good luck for the exam tomorrow - I'm sure you'll do well.
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7 years ago
#10
If you split line ab equally with a line from the centre you make two triangles right. Now let look at triangle aoc (were c is the perpendicular bisector from point o) i did some calculations and ended up with 8 . Im most likely wrong so could you go through your steps please and thank you

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7 years ago
#11
(Original post by zohaib029)
If you split line ab equally with a line from the centre you make two triangles right. Now let look at triangle aoc (were c is the perpendicular bisector from point o) i did some calculations and ended up with 8 . Im most likely wrong so could you go through your steps please and thank you

Samsung > Apple
You've got the right idea but you haven't posted your working so I don't know where you've gone wrong.

The key step is to notice that OC=r-4 where r is the radius of the circle. Also, AO=r. So you have a right-angled triangle AOC with lengths 6, r-4 and r so you can use Pythagoras to find r.
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7 years ago
#12
I know were Im wrong . I made an assumption which isn't true. But im stumped.help me out please

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7 years ago
#13
Oh... Thank you very much

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7 years ago
#14
(Original post by zohaib029)
I know were Im wrong . I made an assumption which isn't true. But im stumped.help me out please

Samsung > Apple
Do you understand my last post? Can you see why OC=r-4 ?

So you have a right-angled triangle where the hypotenuse is r and the other two sides are 6 and r-4.

Use Pythagoras to write down an equation and post it here.
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7 years ago
#15
Sorry .you dint read my post before. Thanks again any way. Also if you don't mind me asking how old are you. Surely you do a level maths or summing

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7 years ago
#16
(Original post by zohaib029)
Sorry .you dint read my post before. Thanks again any way. Also if you don't mind me asking how old are you. Surely you do a level maths or summing

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I'm a maths teacher.
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7 years ago
#17
Oh ok i was starting to worry as i thought that if another Gcse student could do that and i couldnt i wasn't as good as i thought( at the moment I've got 119 /120 ums in paper one and 116/120 in paper 2)

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1 year ago
#18
I came across the question today and i dont get how OC=r-4
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