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501. In figure, AB > AC, BO and CO are the bisectors of ∠B and ∠C respectively. Show that OB > OC.

Given: AB > AC, BO and CO are the bisectors of ∠B and ∠C respectively.
To Prove: OB > OC
Proof: ∵ AB > AC | Given
∴ ∠ACB > ∠ABC
| Angle opposite to longer side is greater

$rightwards double arrow space space 1 half space angle A C B greater than 1 half angle A B C rightwards double arrow space space space angle O C B space greater than space angle O B C therefore space space space space O B greater than O C$

| Side opposite to greater angle is longer