Dhaka Regional 2015 Higher Secondary/9 Secondary/9

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Kazi_Zareer
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Dhaka Regional 2015 Higher Secondary/9 Secondary/9

Unread post by Kazi_Zareer » Sat Jan 09, 2016 9:06 pm

$ \Gamma _{1}$, $\Gamma _{2}$ are two circles with radius $\surd{2}$ and $2$ unit consecutively. The distance between their centres is $2\surd{2}$ unit. The two circle intersect at point $P$ and $Q$. $PR$ is a chord of $\Gamma _{2}$ which is bisected by $ \Gamma _{1}$. $PR$ =?

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Phlembac Adib Hasan
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Re: Dhaka Regional 2015 Higher Secondary/9 Secondary/9

Unread post by Phlembac Adib Hasan » Sun Jan 10, 2016 4:31 pm

At a first glance, I think co-ordinate bashing provides the the most obvious solution. If $O_1$ and $O_2$ are the centers of the two circles, set $O_1O_2$ and $PQ$ as the $X$ and $y$ axises, resp. and do some routine calculation.
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