## Dhaka Higher Secondary 2011/10

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Please

**don't post problems (by starting a topic)**in the "Higher 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 Higher Secondary 2011/10

A point $P$ is chosen inside a right angled triangle $ABC$, perpendicular lines $PS$, $PQ$ and $PR$ are drawn from $P$ on $AB, BC$ and $AC$. $PR = 1, PQ = 2$ and $PS = 3$ and $\angle RPS = 150^{\circ} $. The length of $ AB$ can be written in the form $x \sqrt y +z$ where $x, y, z$ are integers. Find $ x + y + z$.

### Re: Dhaka Higher Secondary 2011/10

*"Go down deep enough into anything and you will find mathematics." ~Dean Schlicter*

### Re: Dhaka Higher Secondary 2011/10

I've got 8.

ABC=APC+BPC+BPA

1/2 AB*AC=1/2 AC*1+1/2*2*BC+1/2*3*AB

AB=1+ 2*BC/AC+3*AB/AC

=1+2cos60+3tan60

=1+1+3*(3)^(1/2)

so x+y+z=8

akashe shurjota othe nirobe

ABC=APC+BPC+BPA

1/2 AB*AC=1/2 AC*1+1/2*2*BC+1/2*3*AB

AB=1+ 2*BC/AC+3*AB/AC

=1+2cos60+3tan60

=1+1+3*(3)^(1/2)

so x+y+z=8

akashe shurjota othe nirobe

### Re: Dhaka Higher Secondary 2011/10

Ibrahim, it's expected that you use LATEX in this forum

And draw a diagram and you should have the explanation for why your answer is incorrect

And draw a diagram and you should have the explanation for why your answer is incorrect

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

### Re: Dhaka Higher Secondary 2011/10

I am using on mobile, so i can't using latex. Plz explain....