Properties of Triangles 3 Question 13

13. The sides of a triangle inscribed in a given circle subtend angles α,β and γ at the centre. The minimum value of the arithmetic mean of cosα+π2,cosβ+π2 and cosγ+π2 is ….

(1987,2M)

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Answer:

Correct Answer: 13. 32

Solution:

  1. Since, sides of a triangle subtends α,β, γ at the centre.

Now, arithmetic mean

=cosπ2+α+cosπ2+β+cosπ2+γ3

As we know that, AMGM, i.e.

AM is minimum, when π2+α=π2+β=π2+γ

or

α=β=γ=120

Minimum value of arithmetic mean

=cosπ2+α=cos(210)=32



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