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in Co-ordinate geometry by (63.5k points)

In a triangle ABC, let angles A, B, C are in G.P. with common ratio 2. If circum radius of triangle ABC is 2, then find the value of (b-1 + c-1 - a-1)

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Best answer

A = x, B = 2x, C = 4x 

⇒ 7x = 180

x = 180/7; c  is obtuse angle

2R = 4 = a/sinA = b/sinB = c/sinC;

sinC = sin3A

- 1/a + 1/b + 1/c = 1/4[1/sinB + 1/sinC - 1/sinA]

= 1/4[1/(3A - 4sin3A) + 1/sin2A - 1/sinA] = 1/4sinA

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