incentre...

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 Î”ABC is.......

2) slope of BC is........

3) if pt.A lies above X-axis and area of Î”ABC is 30sq.units, then the inradius of Î”ABC is......

1 Answers

I 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.

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