BdMO National Higher Secondary 2007/1

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BdMO
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BdMO National Higher Secondary 2007/1

Unread post by BdMO » Sun Feb 06, 2011 10:13 pm

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

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nafistiham
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Re: BdMO National Higher Secondary 2007/1

Unread post by nafistiham » Mon Jan 23, 2012 3:41 pm

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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