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Length of AB with a circle and a tangent watch

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1. The circle (x-1)^2 + (y-1)^2=4 has a tangent at point A that also passes through the point B (6, 0). Find distance AB. Really struggling with this question, can anyone show me the method?
Hint: draw apicture…the tangent to a circle is perpendicular to the radius …. Pythagoras….

Question came with a hint
2. (Original post by LukeMontgomery)
The circle (x-1)^2 + (y-1)^2=4 has a tangent at point A that also passes through the point B (6, 0). Find distance AB. Really struggling with this question, can anyone show me the method?
Hint: draw apicture…the tangent to a circle is perpendicular to the radius …. Pythagoras….

Question came with a hint
What does the sketch you've drawn show? Which two side do you know the length of already (one of which has to be worked out?)
3. (Original post by SeanFM)
What does the sketch you've drawn show? Which two side do you know the length of already (one of which has to be worked out?)
All I know is that the centre of the circle is 1,1 and the radius is 2, I don't understand how to work out the equation of the tangent that goes through 6,0.
4. (Original post by LukeMontgomery)
All I know is that the centre of the circle is 1,1 and the radius is 2, I don't understand how to work out the equation of the tangent that goes through 6,0.
If we call C the centre of the circle and CAB the triangle you're interested in... AB is the length we want. What is CA? What is CB? What can we do with those things?
5. (Original post by SeanFM)
If we call C the centre of the circle and CAB the triangle you're interested in... AB is the length we want. What is CA? What is CB? What can we do with those things?
Are you trying to help me through it or do you not understand either, difficult to tell through text!
6. (Original post by LukeMontgomery)
Are you trying to help me through it or do you not understand either, difficult to tell through text!
7. (Original post by SeanFM)
Is the answer root 26? 5^2 + 1^2=26 then square root 26?
8. (Original post by LukeMontgomery)
Is the answer root 26? 5^2 + 1^2=26 then square root 26?
Yes one side is root 26, what is the other known side
9. (Original post by AlexS101)
Yes one side is root 26, what is the other known side
Didn't I just state all 3 sides, 5,1, and root 26, I feel like im missing something.
10. (Original post by LukeMontgomery)
Is the answer root 26? 5^2 + 1^2=26 then square root 26?
That's the length of CB, which we need but isn't the final answer? Can you see why it's useful and what to do next?
11. (Original post by SeanFM)
That's the length of CB, which we need but isn't the final answer? Can you see why it's useful and what to do next?
Length CB is what I thought was root 26.
12. (Original post by LukeMontgomery)
Length CB is what I thought was root 26.
Correct. If you look at the diagram you've sketched you'll see what CB is (C is the centre of the circle, B is the given point and CB is the line between them, and ABC forms a right-angled triangle. Which side are you looking for in the question? What two sides do you know now? (One is CB). So where do you go from there?
13. (Original post by SeanFM)
Correct. If you look at the diagram you've sketched you'll see what CB is (C is the centre of the circle, B is the given point and CB is the line between them, and ABC forms a right-angled triangle. Which side are you looking for in the question? What two sides do you know now? (One is CB). So where do you go from there?
You're looking for the tangent line, I know CB and CA, I don't know where you go from there.
14. (Original post by LukeMontgomery)
You're looking for the tangent line, I know CB and CA, I don't know where you go from there.
You're almost there

SO ABC is a right angled triangle.. you've got CB and CA... you want AB...
15. (Original post by SeanFM)
You're almost there

SO ABC is a right angled triangle.. you've got CB and CA... you want AB...
Is it root 26 squared (so 26) - 2 squared (4) = 22 length is root 22?
16. (Original post by LukeMontgomery)
Is it root 26 squared (so 26) - 2 squared (4) = 22 length is root 22?
Yes, that should be correct. Well done
17. (Original post by SeanFM)
Yes, that should be correct. Well done
Would it be ok if you could right out the whole method, its ok if you don't, now that I understand it!
18. (Original post by LukeMontgomery)
Would it be ok if you could right out the whole method, its ok if you don't, now that I understand it!
If you look back at my previous hints you'll probably be able to piece it together, along with the hints already given in the question.
19. (Original post by SeanFM)
If you look back at my previous hints you'll probably be able to piece it together, along with the hints already given in the question.
Ok, cheers, never thought I could do this question, thank god for this website! Couldn't find anything anywhere else.
20. That was pretty epic support

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