Question

Given ∆ABC, OB and OC are bisectors of ∟EBC and ∟DBC respectively. Prove that ∟BOC = 90 + 1/2∟A

pls explain

Answer 1

Proved ∠BOC = 90° - A/2  if  OB and OC are bisectors of ∟EBC and ∟DBC respectively

Step-by-step explanation:

OB and OC are bisectors of ∠EBC and ∠DCB respectively

∠CBO = ∠EBO = ∠EBC/2

∠BCO = ∠DCO = ∠DCB/2

∠EBC = x + z    => ∠CBO = (x + z)/2

∠DCB = x + y   => ∠BCO = (x + y)/2

in Δ OBC

∠CBO + ∠BCO + ∠BOC = 180°

=> (x + z)/2 + (x + y)/2 + ∠BOC = 180°

=> (x + y + z)/2 + x/2 + ∠BOC = 180°

=> 180°/2 + x/2 + ∠BOC = 180°

=> ∠BOC = 90° - x/2

=> ∠BOC = 90° - A/2

QED

Proved

Learn More :

In a triangle abc, ob and oc are the angle bisectors of b and c

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https://brainly.in/question/12931931

Answer 2

Answer:

see the above answers it is correct