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in Co-ordinate geometry by (63.5k points)

If ‘O’ is the circum centre of the ∆ABC and  R1, R2 and R3 are the radii of the circum circles of triangle OBC, OCA and OAB respectively then a/R1 + b/R2 + c/R3 has the value equal to

(A) abc/2R2

(B) R3/abc

(C) 4∆/R2

(D) ∆/4R2

1 Answer

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Best answer

Correct option (C) 4∆/R2

Explanation:

∠AOB = 2∠C = 2C

OA = OB = R

AB/sin∠ AOB = 2R1

R1 = c/2sin2c

L.H.S. = 2[sin2A + sin2B + sin2C] 

= 2[2 sin(A + B) cos(A – B) + 2 sin C cos C] 

= 4 sin C[cos(A – B) ± cos(A + B)] = 8 sinA sinB sinC

= 8(1/2absinC)(1/2bcsinA)(1/2casinB)

= 8a/a2b2c2 = 64∆3/a2b2c2 = 4∆/R2

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