## Dhaka Secondary 2011/6

**Forum rules**

Please

**don't post problems (by starting a topic)**in the "Secondary: Solved" forum. This forum is only for showcasing the problems for the convenience of the users. You can post the problems in the main Divisional Math Olympiad forum. Later we shall move that topic with proper formatting, and post in the resource section.

### Dhaka Secondary 2011/6

The diagonal $AB$ in quadrilateral $ADBC$ bisects the angle $CBD$. $DB$ and $DA$ are tangent to the circumcircle of triangle $ABC$ at points $A$ and $B$. The perimeter of triangle $ABC$ is $20$ and perimeter of triangle $ABD$ is $12$. Find the length of $BD$.

### Re: Dhaka Secondary 2011/6

I'm a bit sad seeing that people are not trying this problem. It's one of my favourite. As a divisional problem, it takes good count of your geometric senses and algebraic capabilities

"Je le vois, mais je ne le crois pas!" - Georg Ferdinand Ludwig Philipp Cantor

### Re: Dhaka Secondary 2011/6

I've solved it n my ans is (36/11)......I'm sorry that I cant post a full solution because I cant use LATEX yet. I'll try to learn it soon. My procedure was to show tringle ABC and triangle ABD are both isosceles and similar to each other.

- Tahmid Hasan
**Posts:**665**Joined:**Thu Dec 09, 2010 5:34 pm**Location:**Khulna,Bangladesh.

### Re: Dhaka Secondary 2011/6

i think it's $\frac{36}{11}$

i did something with the ecantor brittangshostho thingyy.

i did something with the ecantor brittangshostho thingyy.

বড় ভালবাসি তোমায়,মা

### Re: Dhaka Secondary 2011/6

Tahmid: Please post your solution!

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please

Please

**install LaTeX fonts**in your PC for better looking equations,**learn****how to write equations**, and**don't forget**to read Forum Guide and Rules.- Tahmid Hasan
**Posts:**665**Joined:**Thu Dec 09, 2010 5:34 pm**Location:**Khulna,Bangladesh.

### Re: Dhaka Secondary 2011/6

for that i'll have to draw the pic but i don't know how to post that here.

so if any1 could give a pic i' gladly give the soln

so if any1 could give a pic i' gladly give the soln

বড় ভালবাসি তোমায়,মা

### Re: Dhaka Secondary 2011/6

Posting diagrams is easy. Just create a diagram and attach it with the post

(There is an "upload attachment" option below post reply editor...however you must use the "full editor" to get this option.)

(There is an "upload attachment" option below post reply editor...however you must use the "full editor" to get this option.)

"Inspiration is needed in geometry, just as much as in poetry." -- Aleksandr Pushkin

Please

Please

**install LaTeX fonts**in your PC for better looking equations,**learn****how to write equations**, and**don't forget**to read Forum Guide and Rules.### Re: Dhaka Secondary 2011/6

i find ABD isosceles.how did you get ABC as isosceles?

**Try not to become a man of success but rather to become a man of value.-Albert Einstein**

### Re: Dhaka Secondary 2011/6

how 2 get similarity???

**Try not to become a man of success but rather to become a man of value.-Albert Einstein**

### Re: Dhaka Secondary 2011/6

$ABD$ and $ABC$ are both isosceles. $\angle BAD=\angle ACB$ (ekanttor brittangshostho kon),

so $\angle ACB=\angle ABD=\angle BAD=\angle ABC$

so in triangle $ABC$ and $ABD$

$\angle ABC=\angle ABD$

$\angle ACB=\angle BAD$

$\angle BAC=\angle ADB$

so $\angle ACB=\angle ABD=\angle BAD=\angle ABC$

so in triangle $ABC$ and $ABD$

$\angle ABC=\angle ABD$

$\angle ACB=\angle BAD$

$\angle BAC=\angle ADB$