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# Circle Geometry watch

1. Can I please ask for your help? I've been given a question, and I cannot solve it. The length of the Tangents from point (4,K) to the circle X^2 + Y^2 = 9 are 4 root 2 (root 32) Find all possible values of the constant K. I can't solve this. Can someone please help?? Thanks. Domo
2. (Original post by van.domo)
Can I please ask for your help? I've been given a question, and I cannot solve it. The length of the Tangents from point (4,K) to the circle X^2 + Y^2 = 9 are 4 root 2 (root 32) Find all possible values of the constant K. I can't solve this. Can someone please help?? Thanks. Domo

From your diagram, you should be able to work out the distance from the point (4,k) to the centre of the circle, without involving k.

Can you take it from there?
3. Alright Mate. OK. The lengths of the tangents are (32)^1/2find all possible K Values?? Let P be P(4,K) C(0.0) PC is the distance from the origin to point P. Therefore, PC^2 = (4-0)^2 + (K-0)^2, PC^2 = (4)^2 + K^2. PC^2= K^2+16, PC^2 is the hypotenuse. AC is the radius to the contact point of the tagent. PA is the length of the tangent. Therefore, using P. Theorem. PC^2 = AC^2 + PA^2. K^2 + 16 = (3)^2 + ((32)^1/2)^2. K^2+16= 9 + 32, K^2 + 16= 41, K^2 = 41-16, K^2= 25 therefore, K= +/- (25^1/2, K= + or - 5. I'm asking the whole world for the answers and end up giving them the answers. I just got the hypotenuse formula mixed up. Thanks ever so much for your interest and help, it's appreciated. regards. domo
4. (Original post by van.domo)
Thanks ever so much for your interest and help, it's appreciated. regards. domo
No problem. Yep, k=+/- 5.

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