(1) Direct proof:

∫ Bo shares ∠ Agricultural Bank of China, CO shares ∠ACB.

∴∠obc= 1/2∠abc,∠ocb= 1/2∠acb

∴∠BOC

= 180 -∠OBC-∠OCB

= 180- 1/2∠ABC- 1/2∠ACB

= 180 - 1/2(∠ABC+∠ACB)

= 180- 1/2( 180-∠A)

= 180 -90 + 1/2∠A

=90 + 1/2∠A

(2) extend BO to AC at point d.

∫∠BOC is the outer corner of △OCD.

∴∠BOC=∠OCD+∠ODC

∫∠ODC is the outer corner of △ABD.

∴∠ODC=∠ABD+∠A

∫ Bo shares ∠ Agricultural Bank of China, CO shares ∠ACB.

∴∠abd= 1/2∠abc,∠ocd= 1/2∠acb

∴∠BOC

= ∠ obsessive-compulsive disorder +∠ODC

=∠OCD+∠ABD+∠A

= 1/2∠ACB+ 1/2∠ABC+∠A

= 1/2(∠ACB+∠ABC)+∠A

= 1/2( 180 -∠A)+∠A

=90 - 1/2∠A+∠A

=90 + 1/2∠A

(3) Connect AO and extend the intersection with BC at point E..

∫∠BOE is the outer corner of △ABO.

∴∠BOE=∠ABO+∠BAO

∫∠COE is the outer corner of △ACO.

∴∠COE=∠ACO+∠CAO

∫ Bo shares ∠ Agricultural Bank of China, CO shares ∠ACB.

∴∠abo= 1/2∠abc,∠aco= 1/2∠acb

∴∠BOC

=∠BOE+∠COE

=∠ABO+∠BAO+∠ACO+∠CAO

=1/2 ∠ ABC+1/2 ∠ ACB+∠ Bao+∠ Cao

= 1/2(∠ABC+∠ACB)+∠A

= 1/2( 180 -∠A)+∠A

=90 - 1/2∠A+∠A

=90 + 1/2∠A

Expand knowledge:

What is geometric proof?

Mathematically, proof is the process of deducing some propositions from axioms and theorems in a specific axiomatic system according to certain rules or standards, which plays a role in reducing the amount of calculation. Compared with evidence, mathematical proof generally relies on deductive reasoning rather than natural induction and empirical reasoning. The proposition derived in this way is also called theorem in this system.

Reference: Baidu Encyclopedia Reference.