Q. 84.0( 4 Votes )
O is an interior
Answer :
Given: ΔABC, O is an interior point of ΔABC
To prove that ∠BOC > ∠BAC
The figure for the given question is as shown below,
Now in ΔABC,
We know in a triangle the sum of all three interior angles is equal to 180°.
So in this case,
∠BAC + ∠ACB + ∠ABC = 180°………(i)
But from the above figure,
∠ABC = ∠ABO + ∠OBC………(ii)
And also,
∠ACB = ∠ACO + ∠OCB…….(iii)
Substituting equation (ii) and (iii) in equation (i), we get
∠BAC + (∠ACO + ∠OCB ) + ( ∠ABO + ∠OBC ) = 180°
⇒ ∠OBC + ∠OCB = 180° - ∠BAC - ∠ACO - ∠ABO………(iv)
Now consider ΔBOC,
We know in a triangle the sum of all three interior angles is equal to 180°.
So in this case,
∠BOC + ∠OCB + ∠OBC = 180°
Substituting equation (iv) in the above equation, we get
∠BOC + (180° - ∠BAC - ∠ACO - ∠ABO ) = 180°
⇒ ∠BOC = 180° - (180° - ∠BAC - ∠ACO - ∠ABO )
⇒ ∠BOC = ∠BAC + ∠ACO + ∠ABO
⇒ ∠BOC > ∠BAC
Hence proved
Rate this question :






















In ΔABC, AC >
West Bengal - MathematicsIn ΔABC, AD is pe
West Bengal - MathematicsIn ΔPQR, PQ >
West Bengal - MathematicsIn a quadrilatera
West Bengal - MathematicsPallabi and Siraj
West Bengal - MathematicsThe internal bise
West Bengal - MathematicsLet’s prove that
West Bengal - MathematicsIn Δ<span lang="E
West Bengal - MathematicsLet’s write the v
West Bengal - MathematicsLet's measure the
West Bengal - Mathematics