Sine and Cosine

For discussing Olympiad level Geometry Problems
tanmoy
Posts:312
Joined:Fri Oct 18, 2013 11:56 pm
Location:Rangpur,Bangladesh
Sine and Cosine

Unread post by tanmoy » Thu Feb 26, 2015 3:36 pm

If $c=b+\frac{1} {2}a$(where $a,b,c$ are the lengths of the sides $BC,CA,AB$,respectively of triangle $ABC$) and $P$ is a point on $BC$ such that $BP:PC=1:3$,prove that $\angle ACP=2\angle APC$
"Questions we can't answer are far better than answers we can't question"

Tahmid
Posts:110
Joined:Wed Mar 20, 2013 10:50 pm

Re: Sine and Cosine

Unread post by Tahmid » Thu Feb 26, 2015 7:44 pm

very cool :P
need to prove $sin \angle C=2sin \angle APC cos \angle APC$

find the value of $cos \angle APC$ by cosine rule in triangle $APC$
then use stewart's theorem to find $AP^{2}$ .

plugging them into $2sin \angle APC cos \angle APC$ and just manipulate .

tanmoy
Posts:312
Joined:Fri Oct 18, 2013 11:56 pm
Location:Rangpur,Bangladesh

Re: Sine and Cosine

Unread post by tanmoy » Thu Feb 26, 2015 8:44 pm

Tahmid wrote:very cool :P
Actually cool and easy. :P
"Questions we can't answer are far better than answers we can't question"

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