I am busy writing test-taking strategies for CAT 2007, CAT2008 aspirants and I thought I should meanwhile share a small strange experience that happened to me in 2006. This particular piece was written in 2006 itself and the events described actually happened. This event left a very strong impression on me because from that day onwards I started solving most of the problems mentally and without using pen or paper.

My day had ended and I was relaxing in my office with two colleagues when one of them popped this question:

ABCD is a trapezium with AB and CD as the longer and shorter of the two parallel sides, respectively. A circle is drawn with AB as diameter such that it touches the side CD and bisects the sides AD and BC. What are the angles of the trapezium?

As I saw the problem, the first thing that was obvious to me, as it would be obvious to any average person, that everything was symmetrical i.e. the sides AD and BC were inclined at the same angle to AB, ABCD was an isosceles trapezium, and that the circle touched CD at its midpoint. So far so good. Now what?

My next inspiration came after a couple of pencil drawings. It looked like the figure shown below:

As AB is the diameter of the circle angle AEB = 90°. E is the midpoint of AD. In triangle ABD, since E is the midpoint and BE is perpendicular to AD, triangle ABD is an isosceles triangle with AB = BD.

What next?

I could not go further than this at that moment. I left it there, deciding to visit the problem again at home in the evening.

I sat after dinner to look at the problem again. The good thing about the problem was the friendly feeling it was giving that the solution was right at the corner of my eye, and that I only had to see it in order to solve the problem. My hopes didn’t seem to be well-founded however. After several attempts, I was nowhere near to solving the problem.
 

My next try yielded the following result:

Let CD touch the circle at P.
Let perpendiculars dropped from P and D on AB meet AB at O and Q respectively.
Let DE = EA = x.

It was clear that I was lost. I was nowhere near to finding the finding the solution. I switched off the lights and went to sleep thinking about the problem.

What happened next was bizarre. In my dream, I could clearly see the problem that I was trying to solve with the whole figure right in front of my eyes. Not only that, I had taken a completely new approach to solving the problem. In my mind, I found myself drawing the figure shown below:

I knew that ABD was an isosceles triangle with AB = BD. Hence AB = BD = 2r.
P and F were midpoint of DC and BC. Therefore, PF // BD in triangle DBC.
Also, PF = BD/2 = r.
Let O be the centre of the circle. Hence, in triangle PFO, PO = FO = PF = r.
--> angle FOP = 60° --> angle FOB = 30° [angle POA = 90°]
In --> triangle FOB, FO = BO = r and angle FOB = 30° -->  angle OAE = 75°.

Hence, the angles of the trapezium are 75° and 105°.

I woke up with a start. I had solved the problem. But now I had a new problem to solve:

HOW DID I MANAGE TO SOLVE A PROBLEM IN MY DREAM?!!!!!!!!!!!

confessions of a beautiful mind eh?? 

keep rocking!!

Excellent & impressive.

Madhukar

TG,

I seriously wish the frequency of your lessons is more ....

when u were awake ur brain was under your control and hence you were guiding it .but when in dreams , your brain has got freewill. It had a solution for it and showed it to you when you were willing to accept it . I believe that our brain is the key to all of the mysteries of this universe and maybe it is the GOD. The real powers of brain are still unfathomed .

But i sincerely hope that i get my answers right there in exam and not in dreams .That's where the objectivity lies.

Abhinav.

This is something ..most of us has observed . TG ..now going back to your lines " This event left a very strong impression on me because from that day onwards I started solving most of the problems mentally and without using pen or paper.
"

Now when are you going to tell us , how you used this power in solving the questions mentally , hope you don't go to sleep after every problem Just kidding

it actually happens...when i was in 10th class..i did the complete ratio and proprotion chapter in my dreams itself and there was only one question that i was nt able to solve which i solved next day...

So stay tuned...to do all tough questiond in dreams if cracking CAT is in dreams

HI TG.. i could not understand how ABD is an isosceles triangle with AB = BD?

will u please help me with that....

amresh

For amaresh .

It's simple  dear . angle AEB is 90 since angle in semicircle ; and E is midpoint of AD(as per question ) then ABD has to be an isosceles triangle since only in an isosceles the median wud be perpendicular to other side .

Thanks ,

Abhinav.

Hi TG

I dont know how u ws able to solve the problem in dream, the good thing is u was able to Solve.

I have a concern..Print out of ur lessons doesnt fit into A4 size paper i did all settings still m not able to take the print properly.

 CAn u Please do something about it?

Thanks

TG FAN

Hi! Eshika,

I am presently working as Officer in a Public Sector Bank for 2.5 years. I have also done diploma in electrical engeering. Now I want to pursue MBA (Correspondance ) plz guide me which institute will be suitalble for me. I am also taking CAT 2007.

Thanks

Tg

Isit posibel 2 give us a low down into the pattern of exams lik xat iift n jmet snap fms  last year .. i have been busy for the last 1 yr n lost track of the cat worls .. would b nice if any 1 has the q papers for the same althpugh i dont think these papers are given to us after the exam

Cheers

S

I hope ill start seeing the problems in my dreams too. Isnt it amazing when you finally realize your single purpose in this life... And that you have a suppoting family to boot ... who never lose the faith in you  inspite of repeated and hopeless failures? I am Kohinoor Biswas and im going to IIM - A 2009-11 batch.

PLAY BALL!!!

hi guru,

how to 'use' my subconscious mind to my potential advantage, will i get 'cooperation' from it during 'that' 2-and-a half hour.