# If in a triangle A=(1,10),circumcenter=(-1/3,2/3) and orthocentre =(11/3,4/3) then the co-ordinates of the side opposite to A is:

siddharth gupta
28 Points
9 years ago
STEP 1:USE THE CONCEPT THAT CENTROID DIVIDES THE LINE SEGMENT JOINING ORTHOCENTRE.
AND CIRCUMCENTRE IN THE RATIO 2:1 CALCULATE THE COORDINATES OF CENTROID(G) AS (1,8/9).
STEP 2:CENTROID=((X1+X2+X3)/3,(Y1+Y2+Y3)/3) CALCULATE X3+X2=2 AND Y3+Y2=-22/3.
STEP 3: USING THESE VALUES OBTAIN MID-POINT OF BC,D=(1,-11/3).
STEP 4:CALCULATE THE DISTANCE BETWEEN A AND CIRCUMCENTRE =CIRCUMRADIUS=R=(800/9)1/2 AND DISTANCE BETWEEN CIRCUMCENTRE AND D=K=(185/9)1/2.
STEP 5:CALCULATE THE SLOPE OF SEGMENT JOINING CIRCUMCENTRE AND D= -13/4.
THIS SEGMENT IS PERPENDICULAR TO BC i.e SLOPE OF BC=4/13 =tan(m).
STEP 6: CALCULATE sin(m) AND cos(m) AND USE PARAMETRIC EQUATION
(X-X1)/cos(m)=(Y-Y1)/sin(m)=(+-)r.(distance to be moved on line)
calculate r using pythagoras theorem =(205/3)1/2.PUT POSITIVE SIGN OFr FOR ONE AND NEGATIVE FOR OTHER COORDINATE TO OBTAIN B AND C.