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vipul agrawal Grade:
        


ABC is a triangle inscribed in a circle, AC being the diameter of the circle. The length of AC is as much more than the length of BC as the length of BC is more than the length of AB. Find AC:AB.

6 years ago

Answers : (2)

Priyansh Bajaj AskiitiansExpert-IITD
30 Points
										



Dear Vipul,


Solution:- Given, AC = a BC and BC = a AB. We want to find AC: AB  = a2


Since, AC is the diameter of the circle, it subtends 900 angle at B. Let, AC = 'd' and angle C be 'x'. Then,


AB = d sinx , and BC = d cosx


So, AC = a BC will give 1 = a cosx     or    cosx = 1/a


And, BC = a AB will give cos x = a sinx


Since, cos x = 1/a, sin x = √(a2 -1) / a


So, 1 = a √(a2 -1)          or         a4 - a2 -1 = 0


On solving quad. eq., we'll get - a2 = (√5 +1) / 2  [ANS]


Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We are all IITians and here to help you in your IIT JEE preparation.

All the best Vipul!!!

Regards,
Askiitians Experts
Priyansh Bajaj



6 years ago
vipul agrawal
19 Points
										

Dear Priyansh,


I would like to correct your solution as follows:-


As per question we have to assume that if AB = X and BC = X+k then AC = BC+ k or AC = X+2k. Then we have to find AC:BC which is equal to 5:3. I would request you to find it out for my son Vipul.


Thanking you.


G.P.Agrawal


F/o Master Vipul Agrawal.

6 years ago
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