IK98
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#1
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#1
How do you solve this problem?
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CaitlinN15
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#2
Report 7 years ago
#2
(Original post by IK98)
How do you solve this problem?
It's a circle theorem- you've got to know your circle theorems to answer it really
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CaitlinN15
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#3
Report 7 years ago
#3
http://www.mathsrevision.net/gcse-ma...ircle-theorems

This site should.help you work your way through it, you've got to identify the correct theorem. I hope this helps

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Azzer11
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#4
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#4
I hate circle theorems. I could start off by saying the triangle is isosceles because the two sides are the same length as they are both diameters of the circle. That also means that the bottom 2 angles of the triangle are equal but after that I'd be stuck...
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KongShou
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#5
Report 7 years ago
#5
90-ACD=OCA=OAC
since OCD is 90deg

AOC=180-(OCA+OAC)=180-2(90-ACD)=180-180+2ACD=2ACD

but
AOC=2ABC

so
2ACD=2ABC
ACD=ABC

Hope this is clear, ask me on any confusing part.
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CaitlinN15
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#6
Report 7 years ago
#6
(Original post by Azzer11)
I hate circle theorems. I could start off by saying the triangle is isosceles because the two sides are the same length as they are both diameters of the circle. That also means that the bottom 2 angles of the triangle are equal but after that I'd be stuck...
Could you also say that a tangent makes an angle of 90degrees with the radius of the circle? As thats part of the theorems. You get marks for writing statments like that..I guess half of these haha

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lerjj
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#7
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#7
(Original post by Azzer11)
I hate circle theorems. I could start off by saying the triangle is isosceles because the two sides are the same length as they are both diameters of the circle. That also means that the bottom 2 angles of the triangle are equal but after that I'd be stuck...
They aren't diameters aas they don't pass through the centre. Isn't this just the alternative segment theorem? Do they expect the proof or just those words?
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IK98
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#8
Report Thread starter 7 years ago
#8
(Original post by KongShou)
90-ACD=OCA=OAC
since OCD is 90deg

AOC=180-(OCA+OAC)=180-2(90-ACD)=180-180+2ACD=2ACD

but
AOC=2ABC

so
2ACD=2ABC
ACD=ABC

Hope this is clear, ask me on any confusing part.
Thank you very much , it is appreciated.
I tried doing something concerning the angles but never thought about calculating AOC
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Azzer11
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#9
Report 7 years ago
#9
(Original post by lerjj)
They aren't diameters aas they don't pass through the centre. Isn't this just the alternative segment theorem? Do they expect the proof or just those words?
Yeah my bad, it is the alternate segment one. Just had a look at the Maths Watch video for circle theorems.
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KongShou
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#10
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#10
(Original post by IK98)
Thank you very much , it is appreciated.
I tried doing something concerning the angles but never thought about calculating AOC
No problem
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contradicta
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#11
Report 7 years ago
#11
Is this requiring us to prove the alternate segment theorem?
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