11mere bhai nine point center is not in the syllabus
SO FORGET IT
I know vectors....but I find these triangle questions difficult.....plz help me in these...
In triangle ABC , O,N,G,O' are circumcentre ,nine point centre ,centroid,orthocentre respectively.AL and BM are perpendiculars from A and B on sides BC and CA respectively.LEt AD be the median and OD is perpendicular to side BC and R be the circumradius of ABC ,then OA=OB=OC=R.
Now in triangle OBD ,OD=RcosA, in triangle ABM , AO' = AM = sec(90-C) {becoz angle O'AM=90-C)
AM cosecC= c cos A/sinC =2R cosA
=>AO'=2OD
If AP is diameter of circumcircle,then answer following questions::
Q1 Prove OA+OB+OC=OO'
Q2 Prove O'A+O'B+O'C=2OO'
Q3 Prove AO'+O'B+O'C=2AO
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11 Answers
1if anyone is going to answer this plz explain it clearly.....so that it will help us to remember also!
11
24baki sab kuch to hai naa.............uske bhi bhool jayen kya???????
aur vaise bhi sab kuch syllabus ka hi nahin padna chahiye........bahar ka bhi kuch padnea chahiye.........
11If u get the 2nd one,u get the 3rd one automatically by triangle law in triangle AOO'.
I'll try n post later.
33mere bas ki baat nahi lag rahi... waise phoorsat me dekhnge...(nine point center nahi pata kya hota hai..)
24are yaar tum sab nine point centre dekh kar ghabra rahe ho........baki sab kuch to dekho.........be positive man,.........[1][1]
24if a circle passes through feet of normal,mid points of sides,mid points of line joining orthocentre O to A,B,C,,,then all these nine points lie on circle called nine point circle
11I think there is some mistake in the ques.
If you add Q1 & Q2 ,you get
(OA+OB+OC) + (O'A+O'B+O'C)=3 OO' BUT
using ∆le law, in ∆le OO'A , ∆le OO'B & ∆le OO'C , we get,
OA-O'A=OO'.........(1)
OB-O'B=OO'..........(2)
OC-O'C=OO'..........(3)
Adding, we get,
(OA+OB+OC) - (O'A+O'B+O'C)=3 OO'
[7][7][7][7][7]
11@eureka....
Few more things.......
Although,P,G,N are not needed,but still,
(i) there is no P in the fig.
(ii) don't you think G and N should be interchanged in the fig.[1][1][1]
In the given fig.,the centroid does notlie on the median[3][3]
I did not understand "....in triangle ABM , AO' = AM = sec(90-C)....."
24mujhe pata hai bahut kuch missing hai aur data confusing hai......[3][3].par meri galti thodi naa hai.......[16]