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Coordinate Geometry Core 1 tangent length help

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1. Hi all!

I'm doing some maths revision for the core 1 exam on Wednesday and I can't seem to get the right answer for this question. The book I'm using is however frequently wrong so I was wondering whether someone else could do the question and see if we get the same answers or whether you get what's in the book. I got the length to be the square root of 57.

Find the length of the tangent from the point (2,5) to the circle x^2 + y^2 -14x - 2y+12=0

Blake
2. (Original post by Blake Jones)
Hi all!

I'm doing some maths revision for the core 1 exam on Wednesday and I can't seem to get the right answer for this question. The book I'm using is however frequently wrong so I was wondering whether someone else could do the question and see if we get the same answers or whether you get what's in the book. I got the length to be the square root of 57.

Find the length of the tangent from the point (2,5) to the circle x^2 + y^2 -14x - 2y+12=0

Blake
Post some working then - I get root(3)
3. (Original post by ghostwalker)
Post some working then - I get root(3)
Will do, the book gets 5?
4. What was the book's answer?
5. I got root 3 also
6. (Original post by ghostwalker)
Post some working then - I get root(3)
The centre of the circle is (7,1) meaning when you have solved the equation of the circle into completed square form you the radius as 4.
I then worked out the length of the line from (2,5) to (7,1) using pythagoras and got that to be sqrt41 (25+16to give 41). Then I used pythagoras again to get the length by doing 41+16 = 57 and then square rooted that for the final length
7. The completed square form gave me a radius square root 38.
8. (Original post by Bigbosshead)
The completed square form gave me a radius 38.
38^1/2
9. (Original post by Bigbosshead)
The completed square form gave me a radius 38.
But 7 squared is 49 and 1 squared is 1 and you have 34 already meaning 50-34=16? And therefore r=4?
10. (Original post by Blake Jones)
But 7 squared is 49 and 1 squared is 1 and you have 34 already meaning 50-34=16? And therefore r=4?
It clearly says 12 not 34. Please post the full question word for word I feel as though you missed something out
11. (Original post by Xenon17)
It clearly says 12 not 34. Please post the full question word for word I feel as though you missed something out
Sorry yes, it is meant to be +34 and then that is the full question word for word, sorry, I got the 12 from the question below, oops!
12. (Original post by Blake Jones)
Sorry yes, it is meant to be +34 and then that is the full question word for word, sorry, I got the 12 from the question below, oops!
lol
13. (Original post by Blake Jones)
Sorry yes, it is meant to be +34 and then that is the full question word for word, sorry, I got the 12 from the question below, oops!
In which case the book's answer of 5 is correct.
14. (Original post by Blake Jones)
The centre of the circle is (7,1) meaning when you have solved the equation of the circle into completed square form you the radius as 4.
I then worked out the length of the line from (2,5) to (7,1) using pythagoras and got that to be sqrt41 (25+16to give 41). Then I used pythagoras again to get the length by doing 41+16 = 57 and then square rooted that for the final length
Should be 41-16 giving 25 and root.

The distance of the point (2,5) to the centre forms the hypotenuse of the triangle, hence subtracting from the 41.
15. (Original post by ghostwalker)
Should be 41-16 giving 25 and root.

The distance of the point (2,5) to the centre forms the hypotenuse of the triangle, hence subtracting from the 41.
woah, you don't need to do this, the circle has point (7,5) at the top (because the radius is 4, and the centre is (7,1)), and the other point given was (2,5). simple as doing 7-2 = 5
16. (Original post by LewisClothier)
woah, you don't need to do this, the circle has point (7,5) at the top, and the other point given was (2,5). simple as doing 7-2 = 5
Methods that work in special situations are useful, but the OP had an issue with working out the length with the more general method, and it was important they get that right. Good spot though.
17. Thank you so much! My diagram wasn't right, I had the length as the hypotenuse! Thanks!

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