## BdMO National Higher Secondary 2007/1

BdMO
Posts: 134
Joined: Tue Jan 18, 2011 1:31 pm

### BdMO National Higher Secondary 2007/1

Problem 1:
Image-problem 1.JPG (6.91 KiB) Viewed 1135 times
In the figure $AB=8,\ BC=7$ and $CA=6.\ \Delta PAB$ is similar to $\Delta PCA$. What is $PC$?

nafistiham
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Joined: Mon Oct 17, 2011 3:56 pm
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### Re: BdMO National Higher Secondary 2007/1

here,
$\frac{PC}{PA}=\frac{AC}{AB}=\frac{PA}{PB}$
suppose, $PC=x$ and $PA=y$
so,
$\frac{x}{y}=\frac{3}{4}=\frac{y}{7+x}$
from which we get $2$ equations,
by solving them we can get $PC$
$\sum_{k=0}^{n-1}e^{\frac{2 \pi i k}{n}}=0$
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