Measure of x problem

Geometric formulae, word problems, theorems and proofs, etc.
hakandragon
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Measure of x problem

Postby hakandragon » Mon Jul 06, 2009 4:57 am

Hi everyone, I hope I have this in the right section.
So, obviously, I've got this problem and I just can't figure it out. (I swear to God I'm a retard when it comes to math; have been since like, 8th grade.)

Given circle with centre O with DE tangent at B.
Find the measure of x.

Image


I did my best to draw out the diagram...I hope it's readable.

Anyways, any help would be loved.

Thanks so much.

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stapel_eliz
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Postby stapel_eliz » Mon Jul 06, 2009 3:19 pm

The line DE is tangent to the circle at point B. The segment OB is a radius line, so, by definition, OB is perpendicular to DE. Then the angle OBD measures 90 degrees.

Since angle FBD measures 31 degrees, then the angle at B in the triangle OBF must measure 90 - 31 = 59 degrees.

By nature of circles and their chords, the triangle OBF is isosceles, so the angle at F is also 59 degrees.

I'll bet you can find the measure of x from here... :wink:

hakandragon
Posts: 13
Joined: Mon May 04, 2009 10:08 pm
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Re: Measure of x problem

Postby hakandragon » Mon Jul 06, 2009 3:24 pm

*gasp* Yes@@ Thank you so much! :clap:


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