# pure 2 aqa

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16 years ago
#1
could anyone do that find the length of the tagent from point p(6,8) to the circle . im sure we werent given enough info - its unanswerable!
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16 years ago
#2
I will give it a go. If you can post the question I am sure someone will be able to help, all the best, Dan
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16 years ago
#3
Ok, just for the record I couldn't manage this one either, and nor could my further maths collegue (both of us had Pure 4 straight after).

We had, earlier in the question, for 5 cute marks out of 60, already established that we have a circle of radius 7, centre (-2, 7).

Find the length of the tangent from the point P(6,8) to the circle.

(4 marks)
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16 years ago
#4
I have just drawn this on paper and come up with the answer. Where the tangent meets the circle you have a right angle formed with the radius to that point so you have a right angled triangle. The short sides are the radius and the one you want. To get the hypotenuse you need the distance between circle centre and P = Sqrt((6--2)^2 + (8-7)^2) = Root 65

Now using Pythagoras' theorem:

you want, (root65)^2 - 7^2 = missing side^2

So the answer is root 16
Therefore 4 units:

Hope this satisfies your curiosity. DAN
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16 years ago
#5
Nice work, tangent is perp to radius I knew, - and had drawn on... annoyingly I couldn't make the link with the lengths and units involved.

Seems quite shoddy that ya get 5 marks for completing the square, and finding the radius and the centre of the circle, and you have to do that much work for 4.
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