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Q.

In ΔABC, the coordinates of the vertex A are 4,−1, and lines x−y−1=0 and 2x−y=3 are the internal bisectors of angles B and C. Then, the radius of the in circle of triangle ABC is

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a

4/5

b

3/5

c

6/5

d

7/5

answer is C.

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Detailed Solution

Incenre 1 is point of intersection of two angle bisectors which is ( 2,1).IA=22+22=22Also, AI=rcosecA2∠BIC=π2+A2or tanπ2+π2=1−21+2or tanA2=3So, r=AIcosecA2=221+1922×310=65

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