Question

For a triangle ABC, the value of cos2A + cos2B + cos2C is least. If its inradius is 3 and incentre is M, then which of the following is NOT correct?

(1) Perimeter of DABC is 18√3

(2) sin2A + sin2B +sin2C = sinA + sinB + sinC

(3) \(\vec {MA}. \vec{MB}\) = 18

(4) area of DABC is \(\frac{27\sqrt 3}2\)

Answer 1

Correct option is (4) area of DABC is \(\frac{27\sqrt 3}2\) 

If cos 2A + cos 2B + cos 2C is minimum then A = B = C = 60°

So △ABC is equilateral

Now in-radius r = 3

So in △MBD we have