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bhars18 · **Quants Teasers -** 24-03-2003, 01:04 PM

I thought I'd start this topic. Hope this would gather momentum as the preparations go into a full swing.

Geometry is my favorite and I want to start off with one in that

A chord of a circle is 36cm long and so is the line drawn perpendicular to it to the major arc. What is its radius.

Regards,
Bharathi.

arcade79 · 24-03-2003, 02:16 PM

Hi Bharathi!!

Well as the subject was Quant Teasers for CAT 2003 so one point all should keep in mind that this has to be solved within a min max... and shud also not b involving a lot of calculations ...

so for the time being I could figure out the following:

The chord of given dimensions cannot b the diameter itself as then the line Perpendicular cant b of equal length in any case...

so in the given case now there would b 2 such perpendicular lines from this chord of equal dimensions...

but this was closing me to one min... so what I can suggest is that diameter has to b greater than 36 cm in n e case.... so as time is running out i wud look for option gr8r than 36...

Frens beleive me I m still trying to solve the prob.. may b I m not that smart in solving this prob, but after having an attempt at this yr CAT , what i just mentioned to solve the prob shouldnt b taken lighlty ...

belive me there cud b a chance taht there cud b only 0ne choice gr8r than 36, then u r thru this ques, even in other case atleast u can cut out a few options....

Chalo I will post the exact soln as soon as i get one..

arcade

bhars18 · 24-03-2003, 03:07 PM

That was a wonderful attempt to solve the problem. I understand that the timing considerations and options are to be considered while cracking CAT. But sometime, if we take time and solve certain problems like this, such ideas will occur to us immediately on the D-day and hence we won't be wasting time then.

This comes under CAT's 'easy' category, once you figure out the diagram for the problem.

Keep sending your questions too. Happy solving.

Regards,
Bharathi

arcade79 · 24-03-2003, 03:26 PM

Quote:

But sometime, if we take time and solve certain problems like this, such ideas will occur to us immediately on the D-day

Well truly agrees with the same.. thats y i said that still trying to solve.. pata nahin i m not able to click that.. may b bcoz rite now i m in office so needs a little conc... will come back 2moro if possible...

My attempt was just to highlight the facts abt time and Intelligent guessing or ruling out options...

arcade

bhars18 · 24-03-2003, 05:19 PM

Sometimes, you know, hardwork also pays back

Regards,
Bharathi.

arcade79 · 24-03-2003, 05:38 PM

No issue on this,... always agreed for hardwork... after all it is not sometims but always paysback

arcade

bhars18 · 24-03-2003, 05:42 PM

That's the spirit! Glad to meet such an optimistic person! Keep going

Regards,
Bharathi

arcade79 · 25-03-2003, 10:30 AM

hey bharathi BTW what is the soln for the prob.. dont leave the story halfway...

bhars18 · 25-03-2003, 11:06 AM

Hi,

Take the chord as AB with centre C. Let O be the centre of the circle. COD is the perpendicular bisector of AB to the major arc. By the problem, AB = CD = 36.

Let the circle be of radius r. So, the lengths OD = OA = OB = r.
OC = CD - OD = 36-r.
In triangle COA (or COB for that matter) applying pythogoras theorem,
(36-r)^2 + 18^2 = r^2

Solving for r, we get r = 22.5.

Hope that helps.

Regards,
Bharathi.

arcade79 · 25-03-2003, 11:21 AM

hey there seems to b some confusion 2 me.. u said line perpendicular and not perpendicular bisector... so the prob started..

and what i said is that there can b 2 perpendiculars on a chord with same length.. i tried this with a circle of radius 2.5 cm and chord of 2 cm.. check that out.. u will find that perpendicular bisector of chord wud b gr8r than 2 cm...

plz cross check..

arcade