in triangle ABC , the incentre is I(1,0). equations of the lines AI , BI, CI are given by x=1 , y+1=x , x+3y=1 respectivly. and cot(A/2)=2
1) eqn of locus of centroid of ΔABC is.......
2) slope of BC is........
3) if pt.A lies above X-axis and area of ΔABC is 30sq.units, then the inradius of ΔABC is......
-
UP 0 DOWN 0 2 1
1 Answers
11I don't think the first part is going to be very nice.....
Anyways for a beginning, here is it....
Let AC intersect X-axis at X'.
A=(1,k).
Since cot A2=2=AIX'I=kX'I, thus X'I=k2.
Co-ordinate of X' is (1-k2,0).
Eqn of Ac is thus known in trms of parameter k, and thus co-ordinate of C can be got in terms of k.
Similarly for B - and thus locus can be got by eleminating the variable k.
That's all that is coming to my mind r8 now.
Nudge me if u have any problem in completing this part.
