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# Geometry Question from GCSE

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1. Geometry Question from GCSE
In the figure ABCD is a square, prove that triangles ADE and CDG are congruent and that AEFG is cyclic.

Calculate the radius of the circumcircle of AEFG and calculate the length of a tangent from B to the circle.

I can do all the parts apart from the last one - any help?
Attached Thumbnails

2. Re: Geometry Question from GCSE
You can easily find the distance from B to the centre of the circle and you know the radius. You can use Pythagoras' theorem to find the length of the tangent from B to the circle.
3. Re: Geometry Question from GCSE
how do i find the distance from B to the centre of the circle - I seem to be going round in circles. I think I've missed something really simple
4. Re: Geometry Question from GCSE
Let D be (0,0) A be (0,15) and C be (15,0). You say you have done all but the last part so you know that the centre of the circle is the midpoint of EG? Let's call it M

So you can find the length BM using Pythagoras theorem.
5. Re: Geometry Question from GCSE
which triangle containing BM is the one you're suggesting I use pythaoras' theorm on?
6. Re: Geometry Question from GCSE
The one with vertices B, M and N, where N is the point where the tangent touches the circle.
7. Re: Geometry Question from GCSE
(Original post by BabyMaths)
You can easily find the distance from B to the centre of the circle and you know the radius. You can use Pythagoras' theorem to find the length of the tangent from B to the circle.
But I need to find the length BM before I do this as the question wants me to find the length BN. You said above that it was easy to find the distance from B to the centre of the circle, but I don't see how to do this initially
8. Re: Geometry Question from GCSE
You said you did all but the last part so you already have the radius?
9. Re: Geometry Question from GCSE
yes I have the radius, but I don't see how that gives me the line BM.
10. Re: Geometry Question from GCSE
Sorry. I was assuming that you know how to find the distance between two points.

You know where B is.
You know where M is.

Now refer to the attached diagram.

11. Re: Geometry Question from GCSE
are you saying that I need to work out the coordinates of M first? I'm not sure how I would do that
12. Re: Geometry Question from GCSE
M is the midpoint of EG. These point are (0,9) and (9,15).

M is .

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Last updated: June 25, 2012
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