BDMO Secondary National 2021 #4

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
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BDMO Secondary National 2021 #4

Unread post by Mehrab4226 » Sat Apr 10, 2021 12:47 pm

\(ABCD\) একটা সমদ্বিবাহু ট্রাপিজিয়াম যেন \(AD=BC\), \(AB=6\) আর \(CD=8\)। \(E\) এমন একটা বিন্দু যেন \(AE\perp EC\) এবং \(BC=EC\)। \(AE\)-এর দৈর্ঘ্যকে \(a\sqrt{b}\) আকারে লেখা যায় যেখানে \(a\) আর \(b\) পূর্ণসংখ্যা এবং \(b\), \(1\) বাদে অন্য কোনো পূর্ণবর্গ সংখ্যা দিয়ে বিভাজ্য না। \((a-b)\)-এর মান বের করো।

$ABCD$ be an isosceles trapezium such that $AD=BC$,$AB=6$ , and $BC=8$. A point $E$ on the plane is such that $AE\perp EC$ and $BC=EC$. The length of $AE$ can be expressed as $a\sqrt{b}$ where $a$ and $b$ are integers and $b$ is not divisible by any square number other than $1$. Find the value of $(a-b)$.
Last edited by Mehrab4226 on Sun Apr 11, 2021 3:53 pm, edited 1 time in total.
The Mathematician does not study math because it is useful; he studies it because he delights in it, and he delights in it because it is beautiful.
-Henri Poincaré

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Re: BDMO Secondary National 2021 #4

Unread post by MrCriminal » Sun Apr 11, 2021 12:34 pm

\(AE = 4\sqrt(3)\). so (a-b) = 1.

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