Let O be the in-center of a triangle ABC and D be a point on the side BC of ΔABC, such that OD ⊥ BC. If ∠BOD = 60°, then ∠ABC = ?

Question: Let O be the in-center of a triangle ABC and D be a point on the side BC of ΔABC, such that OD ⊥ BC. If ∠BOD = 60°, then ∠ABC = ?

Solution:

Given,
∠BOD = 60°

We know,
∴ ∠BDO + ∠DOB + ∠DBO = 180°
⇒ ∠DBO = 180° - ∠BDO + ∠DOB
⇒ ∠DBO = 180° - 90° - 60°
∴ ∠DBO = 30°

Now,
∠ABC = 2 × ∠DBO
⇒ ∠ABC = 2 × 30°
∴ ∠ABC = 60°