BDMO 2017 National round Secondary 2

Discussion on Bangladesh Mathematical Olympiad (BdMO) National
Facebook Twitter

BDMO 2017 National round Secondary 2

Post Number:#1  Unread postby ahmedittihad » Fri Feb 10, 2017 8:42 pm

$\triangle ABC$ is an isosceles triangle inscribed in a circle with center $O$ and diameter $AD$ and $AB=AC$. The diameter intersects $BC$ at $E$, and $F$ is the midpoint of $OE$. Given that $BD\parallel FC$ and $BC=2 \sqrt[]{5}$, find the length of $CD$.
Frankly, my dear, I don't give a damn.
User avatar
Posts: 147
Joined: Mon Mar 28, 2016 6:21 pm

Re: BDMO 2017 National round Secondary 2

Post Number:#2  Unread postby Ananya Promi » Thu Apr 27, 2017 4:31 pm

Here, $AD$ is perpendicular on $BC$
Hence, $BE=CE$
We can show that $$\triangle$$$BDE$ and $$\triangle$$$CFE$ are congruent.
So, $FE=ED=OF=\frac{1}{3}OD=\frac{1}{3}OB$
In the right angle triangle $OBE$,
in rigth angle triangle $CED$,
User avatar
Ananya Promi
Posts: 18
Joined: Sun Jan 10, 2016 4:07 pm
Location: Naogaon, Bangladesh

Share with your friends: Facebook Twitter

Return to National Math Olympiad (BdMO)

Who is online

Users browsing this forum: No registered users and 3 guests