The alternate segment theorem

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May 2nd 2008, 04:06 AM
zp3929

The alternate segment theorem

this is a well above the standed question for a yr 10 geometry assignment i am working on
http://i286.photobucket.com/albums/l...1/untitled.jpg

so the first thing i did was to draw a diameter from a to a new point g, which the i joined two lines from g to d and e, the next thing i did was to find 3 right angles in the circle so i could try to find a relationship between g,d,a and a,e,d
http://i286.photobucket.com/albums/l.../untitled2.jpg

but now i am kinda stuck

any help would be greatly appreciated

thanks

Zac
May 2nd 2008, 04:38 AM
earboth

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Quote:

Originally Posted by zp3929

this is a well above the standed question for a yr 10 geometry assignment i am working on
http://i286.photobucket.com/albums/l...1/untitled.jpg

...
Zac

I've modified your drawing a little bit.

1. Draw a perpendicular bisector of AD.

2. $|\xi| = |\epsilon|$

3. $\angle(MAB) = 90^\circ$ because the radius is perpendicular to the tangent in the tangent point.

4. $|\alpha| = 90^\circ - |\xi| = 90^\circ - |\epsilon|$

5. $|\tau| = 90^\circ - |\alpha| = 90^\circ - (90^\circ - |\epsilon|) ~\implies~ \boxed{|\tau| = |\epsilon|}$
May 2nd 2008, 04:39 AM
mr fantastic

Quote:

Originally Posted by zp3929

this is a well above the standed question for a yr 10 geometry assignment i am working on

so the first thing i did was to draw a diameter from a to a new point g, which the i joined two lines from g to d and e, the next thing i did was to find 3 right angles in the circle so i could try to find a relationship between g,d,a and a,e,d

but now i am kinda stuck

any help would be greatly appreciated

thanks

Zac

Read this: VICIOUS CIRLES: The Alternate Segment Theorem!

Or this: Circle Theorems

Or even this: http://www.benjamin-mills.com/maths/...rems-proof.pdf (not bad for a student of his age)