Tahlil's blog

Proof of a geometry problem
By Tahlil, 14 years ago, In English

Hello. My friends and I tried to solve this problem of this website.

http://www.gogeometry.com/problem/problem001.htm

But we could not. Can anyone please provide a proof of this problem? Thanks.

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14 years ago, hide # |
 
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Triangles ABC and BDC are similar (have equal angles). So, AC/BC=BC/DC. But AC=2*DC (from statement) and we obtain: BC^2=2DC^2 => BC=sqrt(2)*DC. Then, by law of sines for triangle BDC: BC/sin(135)=DC/sin(x), or sqrt(2)/sin(135) = 1/sin(x) and sin(x) = 1/2. Thus x = 30 degrees.

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    14 years ago, hide # ^ |
     
    Vote: I like it +13 Vote: I do not like it

    Thanks a lot :) Btw I don't know why but I cant vote on your comment!! It says you cannot vote twice. but the vote count isn't increasing!

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