Circle Theorems

Original post by karmacrunch

Hello! I can't find a way to work out this question, I have done everything else on this sheet and I think I might be making a silly mistake!

Here is the question:

The first one seems to be a twisted round version of angles at the centre and circumferences (if you look carefully, they're both subtended by the same arc at the bottom)

For the other one, use the fact that the radii have equal lengths so they make an isoscoles triangle

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Reply 2

MathMeister

They should be touching the circumference. In my opinion, it hasn't printed correctly and is aligned a little. Or they drew it badly in the first place badly. A question in the exam would not be so ambiguous. If you are not convinced, answer it both ways, on circumference and not on the circumference. Mymaths and mathswatchvle are very good resources- as well as the exam boards revision book. I also have a really good resource I will edit into this post when I find it. Here it is... http://bland.in/gcse/newpapers_combined.pdf I'd learn them before doing it. Do the appropriate questions as practice/ use it as exam practice after fully revising. I found it rather useful.

Reply 3

Original post by Arithmeticae

"For the other one, use the fact that the radii have equal lengths so they make an isoscoles triangle" <-- Ahh thanks :smile:

But do you mean for angle S?

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Reply 4

Original post by MathMeister

1. They should be touching the circumference. In my opinion, it hasn't printed correctly and is aligned a little. Or they drew it badly in the first place badly. A question in the exam would not be so ambiguous.

2. If you are not convinced, answer it both ways, on circumference and not on the circumference. Mymaths and mathswatchvle are very good resources- as well as the exam boards revision book. I also have a really good resource I will edit into this post when I find it. Here it is... http://bland.in/gcse/newpapers_combined.pdf I'd learn them before doing it. Do the appropriate questions as practice/ use it as exam practice after fully revising. I found it rather useful.

1. Ah, I was wondering. I'll ask my teacher
2. We've already learnt them (well 4 properly) :tongue:

but thanks!

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Reply 5

Original post by karmacrunch

"For the other one, use the fact that the radii have equal lengths so they make an isoscoles triangle" <-- Ahh thanks :smile:

But do you mean for angle S?

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It's just a printing error, the sides should be touching the circumference and you can clearly see they are both subtended by the bottom arc, only one is at the bottom and one is at the circumference.

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Reply 6

Original post by Arithmeticae

Okay
So both are 41 degrees? I didn't realise that, that counts as well?

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Reply 7

Original post by karmacrunch

Okay
So both are 41 degrees? I didn't realise that, that counts as well?

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T is, I don't think S is :/

What circle theorem are you using?

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Reply 8

Original post by Arithmeticae

T is, I don't think S is :/

What circle theorem are you using?

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That's what I Ithought T=41 degrees
I wasn't using one for that, you said that S & T were subtended by the same arc? Or maybe I misread that.
That's why I said 'I didn't know that counts?' :confused:

I'll look at it again, give me a min sorry!

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Reply 9

Original post by karmacrunch

That's what I Ithought T=41 degrees
I wasn't using one for that, you said that S & T were subtended by the same arc? Or maybe I misread that.
That's why I said 'I didn't know that counts?' :confused:

I'll look at it again, give me a min sorry!

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I meant O and S... :s-smilie:

Reply 10

Original post by Arithmeticae

I meant O and S... :s-smilie:

Oooh... that's why I didn't get I then and you were saying it was most likely a printing error! :facepalm:

Sorry but thank you :biggrin:

Reply 11

Trying to explain a geometry question on here without referencing vertices can be hard as shown in this thread. I'm not entirely sure the OP understood it in the end.

Reply 12

Original post by Arithmeticae

I meant O and S... :s-smilie:

I got S wrong it was 49 degrees because of- Angle subtended at the is twice angle subtended at the circumference. :/

Original post by MathMeister

That's what I said at the beginning! :smile:

Honestly I don't think it was a printing error anymore because of what I said above ^ :redface:

Original post by notnek

Trying to explain a geometry question on here without referencing vertices can be hard as shown in this thread. I'm not entirely sure the OP understood it in the end.

It wasn't too bad don't worry, but the referencing would have helped more. It's fine :smile:

Reply 13

Original post by karmacrunch

Honestly I don't think it was a printing error anymore because of what I said above ^ :redface:

(I think) both helpers were referring to the highest and lowest vertex, both of which are supposed to be on the circumference but are slightly too low (one is just inside the circle and the other is just outside).

I felt like throughout this thread you thought the "printing error" was something else. I may be wrong?

(edited 9 years ago)

Reply 14

Original post by karmacrunch

I got S wrong it was 49 degrees because of- Angle subtended at the is twice angle subtended at the circumference. :/

Honestly I don't think it was a printing error anymore because of what I said above ^ :redface:

It wasn't too bad don't worry, but the referencing would have helped more. It's fine :smile:

Original post by Arithmeticae

The first one seems to be a twisted round version of angles at the centre and circumference

Original post by Arithmeticae

I meant O and S... :s-smilie:

I said that!

(edited 9 years ago)

Reply 15

Original post by notnek

(I think) both helpers were referring to the highest and lowest vertex, both of which are supposed to be on the circumference but are slightly too low or too high.

I felt like throughout this thread you thought the "printing error" was something else. I may be wrong?

No that is what I thought too with the vertices not touching properly.

After finding out the actual answer for angle S I thought that there isn't actually a printing error since I used the circle theorem 'Angle subtended on the centre is twice the angle subtended on the circumference' answer.

(I think) :confused:

Reply 16

Original post by karmacrunch

I'm confused. Which vertices are you referring to.

Reply 17

Original post by Arithmeticae

Arithmeticae

The first one seems to be a twisted round version of angles at the centre and circumference

I said that! :s-smilie:

You did? :0

I didn't understand what you meant by that before! I understand now only because I know which theorem to use.

Which might be what notnek means?
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Reply 18

Original post by notnek

I'm confused. Which vertices are you referring to.

Sorry, I didn't see this!

I meant the vertex at the top and the one at angle S which is slightly over the circumference of the circle. :smile:

Reply 19