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If Two Angles of a Triangle Are Congruent Then the Sides Opposite to Them Are Congruent

In the given ...

Question

In the given figure, AB > AC. If BO and CO are the bisectors of ∠B and ∠C respectively, then
(a) OB < OC
(b) OB = OC
(c) OB > OC

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Solution

(c) OB > OC

AB >AC (Given)
$\Rightarrow ∠ C > ∠ B$
$\Rightarrow \frac{1}{2} ∠ C > \frac{1}{2} ∠ B$
$\Rightarrow ∠ O C B > ∠ O B C$ (Given)
$\Rightarrow O B > O C$

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If Two Angles of a Triangle Are Congruent Then the Sides Opposite to Them Are Congruent

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