## Measure of x problem

Geometric formulae, word problems, theorems and proofs, etc.
hakandragon
Posts: 13
Joined: Mon May 04, 2009 10:08 pm
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### Measure of x problem

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.

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

Anyways, any help would be loved.

Thanks so much.

stapel_eliz
Posts: 1628
Joined: Mon Dec 08, 2008 4:22 pm
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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...

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

*gasp* Yes@@ Thank you so much!