21sorry sir...it will be a,b,c belongs to {1,2,3,....1999}
1)find the number of quadratic polynomials ax2+bx +x,which satisfy the following conditions:
a) a,b,c are distinct b) a,b,c, belongs to {1,2,3,...,1999) c)x+1 divides ax2+bx +x..
2)let ABCD BE A QUADRILATERAL in which AB is parallel to CD;AB=3CD;the area of the quadrilateral is 4.if a circle can be drawn touching all the sides of the quadrilateral ,find its radious..
i just want to verify my answer...1)1996002 2) √3/2
3)can we apply co ordinate geo. in geometry problems in RMO ?like the 2nd one? i mean is it accepted?
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14 Answers
1063) coord. geo is highly discouraged in most olympiad exams .. it may so happen that you get only 20-30 % of the credit if your method is correct.
1well Shubhodip my friend i am getting a the reciprocal of ur answer for the 2nd one.and i didnt use any coordinate geometry and i would love to know what u did so pls post it.k then i used only pure geometry but i also may be wrong i will upload wht i did here pls check and say but the problem is how do u upload a pic over here ?????? sorry about this but i realy dont know
well any way i will tell ya what i did in words hope this helps and let me know how to upload so that i can upload a pic.
first the figure will be a traperizum and a circle inbetween soo the perpendicular height is the diameter of the circle so we can use the area of the trapezium and find realtion betwee side AB and the radius.then draw an other diameter for the circle this time horizondaly so that its parallel to the other sides and then split big trapezium into two smaller onces and sum up the area to 4 u will get anothe relation (this time a different one from before)so there u have it 2 realtion 2 unkowns find the radius.
k thats all
1
ok found it k uploading now
i just now found out the upload option sorry about that.and sorry is its not so clear my i took it from my mob cam.
36Is it important that the height of the trapezium circumscribing the circle will be 2r!
How tell me?
It may be the case that the line joining the point of contacts of the tangents AB and CD
to the circle may not pass through the centre.
Plz explain...
The RMO problems generally need lots of constructions if we solve them by simple
geometry like this one:
Q> Let ABC be a triangle in which AB = AC and LCAB = 900. Suppose M and N
are points on the hypotenuse BC such that BM2 + CN2 = MN2.P rove that
LMAN = 450
21@rahul tangents are perpendicular to the radius drawn to the pt. of contact..
i used a bit trigo in ur question(also did by co ordinated)... can we apply trigo in RMO??
36Surely we can use trigono in RMO!
The solution by trigono to this question requires no constructions.
But if we solve it by plane geometry then it will require loads and
loads of constructions.
36wow! u dunno the meaning of construction..... Right!
well, kisi bhi triangle ke andar ya bahar kuch aur lines introduce karke use solve
karne ki vidhi to construction kehte hein... (maybe clr now)!!
36My above post was a reply to subho's question, "What is construction?".
But he has removed the post.. So don't take that as an illogical one..!
Thank you!!!!