O is the centre of the circle passing through the points A, B and C such that \angleBAO = 30^\circ, \angleBCO = 40^\circ and \angleAOC = x^\circ . What is the value of x ?

RRB Junior Engineer Stage 1 Model Papers 3

Question : 29 of 100

Marks: +1, -0

O is the centre of the circle passing through the points A, B and C such that

∠BAO = 30°, ∠BCO = 40°

and

∠AOC = x°

. What is the value of x ?

Solution:

In ∆AOB
AO = BO (radii of circles)

∴ ∠ABO = ∠BAO = 30º

In ∆BOC

BO = CO (radii of circles)

∴ ∠BCO = ∠OBC = 40º

∠ABC = ∠ABO + ∠OBC

∠ABC = 30° + 40° = 70°

2 × ∠ABC = ∠AOC ⇒ x° = 140

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