Question

If a triangle has its orthocenter at {1,1} and circumcenter {3/2,3/4} and its centroid and nine point circle are (x,y) and (p,q) respectively ,then value of 6x+12y-4p-8q must be????????

Answer 1

H = (1,1)          N= (p, q)          G= (x,y)          O = (3/2, 3/4)

HN = ON        -  N is the mid point of  OH

p = (1+3/2)/2 = 5/4         
q = (1 +3/4)/2 = 7/8

OG = 1/3 OH                  OG : GH = 1 : 2
G divides OH in the ratio of 1 : 2
x = (1 *1 + 2*3/2)/(1+2) = 4/3
y = (1*1+2*3/4)/(1+2) = 5/6

6x  + 12 y - 4 p - 8 q
   =  6 * 4/3 + 12 * 5/6 - 4 * 5/4 - 8 * 7/8
   =  6

Answer 2

Step-by-step explanation:

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