# In the given figure, AB = AC and OB = OC. Then,

Question:

In the given figure, AB = AC and OB = OC. Then, ABO : ∠ACO = ?
(a) 1 : 1
(b) 2 : 1
(c) 1 : 2
(d) None of these

Solution:

(a) 1:1

In $\Delta O A B$ and $\Delta O A C$, we have :

$\mathrm{AB}=\mathrm{AC} \quad$ (Given)

$\mathrm{OB}=\mathrm{OC} \quad$ (Given)

$\mathrm{OA}=\mathrm{OA} \quad$ (Common side)

Thus, $\triangle \mathrm{OAB} \cong \mathrm{OAC} \quad$ (SSS criterion)

i.e., $\angle A B O=\angle A C O$

$\therefore \angle A B O: \angle A C O=1: 1$