Let a , b and c denote the length of sides opposite to vertices A,B and C respectively of a triangle ABC. Let a=6 ,b=10 and the area of triangle is 15 square root 3 If angle ACB is obtuse and if r denotes the radius of the incircle of the triangle then r^2 equals

Answers (1)

Solution:     Delta =frac12ab sin C=15sqrt3=frac12	imes 6	imes 10	imes sin C

                 Rightarrow    sin C=fracsqrt32,    or     C=120^circ

              Now ,     cos C=fraca^2+b^2-c^22ab

           Rightarrow           -frac12=frac36+100-c^2120Rightarrow c=14.

                           2s=a+b+cRightarrow s=15.

             Now ,       r=fracDelta s=frac15sqrt315=sqrt3Rightarrow r^2=3.

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