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tips and tracks for general 2-d.
ritu
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Posted on
20 Sep 2007 12:37:10 IST
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20 Sep 2007 12:37:10 IST
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tips and tracks for general 2-d.
Engineering Entrance , JEE Main , JEE Main & Advanced , Mathematics , Trigonometry
Hiiiiii friends.here's a list of direct formula's which may prove helpful in solving problems of general coordinate system.
 
1.The incentre of the triangle formed by (0,0),(a,0),(0,b) is
   [(ab/a+b+a2+b2),(ab/a+b+a2+b2)].
 
2.If D,E,F are the midpts of the sides BC,CA,AB of triangle ABC,
    the centroid of triangle ABC=centroid of triangle DEF.
 
3.If (x1,y1),(x2,y2) are the 2 vertices of an equilateral triangle,then it's 3rd vertex is [{x1+x23(y1+y2)}/2 , {y1+y2-/+3(x1-x2)}/2].
 
4.If (x1,y1),(x2,y2) are the extremities of the hypotenuse of a rght angled isosceles triangle.then its 3rd vertex is [{x1+x2(y1-y2)}/2 , {y1+y2-/+(x1-x2)}/2].
 
5.If H is the orthocentre of triangle ABC,then A,B,C are the orthocentres of triangle HBC,HCA,HAB respectively.
 
6.If Q is the harmonic conjugate of P w.r.t A.B then AP,AB.AQ are in H.P.
 
7.Nine pt circle-let L,M,N be the feet of the altitudes and D,E,F be the midpts of the sides of triangle ABC.let X,Y,Z be the midpts of AH,BH,CH where H is the orthocentre of the triangle.then L,M,N; X,Y,Z lie on a circle called nine pt circle.
 
8.The centre of the nine pt circle is the midpt of the line segment joining orthocentre and circumcentre.
9.The radius of the nine pt circle of triangle ABC ir R/2 where R is the circumradius.
10.If N is the centre of the nine pt circle,H is the orthocentre,S is the circumcentre and G is the centroid of triangle ABC.then HN:NG=3:1 , HN:NS=1:1 , NG:GS=1:2.
 
11.The circumcentre of the triangle with vertices (0,0),(x1,y1),(x2,y2) is {y2(x12+y12)-y1(x22+y22)}/2(x1y2-x2y1) ,{x2(x12+y12)-x1(x22+y22)}/2(x2y1-x1y2).

Comments (4)
lalasa
Hot goIITian

Joined: 15 Jul 2007 23:32:25 IST
Posts: 141
20 Sep 2007 12:45:28 IST
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good work...helpful for quick review....

SINDHURA KADIYALA
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Joined: 23 Apr 2007 18:54:45 IST
Posts: 341
20 Sep 2007 13:13:53 IST
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nice..........

Apoorva .
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Joined: 18 Jul 2007 19:07:19 IST
Posts: 187
20 Sep 2007 16:40:58 IST
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gud :)

Himanshu
Forum Expert
Joined: 19 Feb 2007 19:24:42 IST
Posts: 3836
19 Dec 2007 02:05:19 IST
0 people liked this

awesome :)


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