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