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really difficult circles question - HSN forum

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really difficult circles question


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#1 craig1e

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Posted 12 March 2007 - 07:20 PM

I need help with this really difficult homework question

I have circle with centre (A,B) and tangents to the circle with the line Y = X and the X axis

I have to prove that a = (1 + root 2)B

My teacher says it is a very hard question and I just can't figure it out. Can anyone help me?

#2 Mr H

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Posted 12 March 2007 - 11:34 PM

That is a tough question!

Here's a clue not an answer! (It will be much more satisfying for you of you can crack it yourself!)

Work out the angle between your tangents and hence its exact value, a simple diagram should do it - you may have one from the question.

Add a line from the origin to (a,b), it will bisect the angle between the tangents and create two congruent right-angled triangles. You need to work with half the angle between the tangents so need a double angle formula for tan! I'm going to leave you to find that bit out for yourself!!! biggrin.gif

If you can get this far then you almost have it cracked!

Substitute your double angle and a bit of surd work will prove that a = (1 + sqrt.gif 2)b

H tends 2 infinity

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