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Geometry..!!

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DeeptiM
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Geometry..!! [#permalink] New post   Updated on: 05 Sep 2011, 01:44
A circle has centre at origin and radius 1. The points X, Y & Z lie on the circle such that the length of arc XYZ is 2/3pie. Whtz the length of line segment XZ?

A) SQRT2
B) SQURT 3
C) 2
D) 2+SQURT3
E) 2+SQURT2

With the length of arc formula, I could sove for the angle but need help with the next steps..pls help..



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Originally posted by DeeptiM on 21 Aug 2011, 05:00.
Last edited by DeeptiM on 05 Sep 2011, 01:44, edited 1 time in total.
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Re: Geometry..!! [#permalink] New post   21 Aug 2011, 07:43
What is the radius of the circle?
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Re: Geometry..!! [#permalink] New post   05 Sep 2011, 01:46
Somebody pls help me with the workings...thnx
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Re: Geometry..!! [#permalink] New post   05 Sep 2011, 05:41
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x / 360 = (2/3pi) / 2pi
x = 120

This is the inner angle, the legs of the triangles will both be equal to the radius (i.e. 1).

Bisect the triangle, we now have two 30-60-90 triangles. Sides will be in proportion 1 : 2 :\(\sqrt{3}\), where 2 is the hypotenuse.

We know the hypotnuse is 1 in this case, so the longest leg of the triangle will be 1/2 \(\sqrt{3}\). We have two of them, so answer is \(\sqrt{3}\).

See badly drawn picture attached.



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Re: Geometry..!! [#permalink]
05 Sep 2011, 05:41
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