MCQ
In the given figure, $AB = AC$ and $OB = OC$. Then, $\angle\text{ABO}:\angle\text{ACO} = ?$ 
- ✓$1 : 1$
- B$2 : 1$
- C$1 : 2$
- DNone of these
✓
Answer
Correct option: A.
$1 : 1$
In $\triangle\text{ABC},$
$\text{AB = AC}\Rightarrow\angle\text{ABC}=\angle\text{ACB}...(\text{i})$
In $\triangle\text{OBC},$
$\text{OB = OC} \Rightarrow\angle\text{OBC}=\angle\text{OCB}...(\text{ii})$
Subtraction (ii) from (i), we get
$\Rightarrow\angle\text{ABO}=\angle\text{ACO}$
So, $\angle\text{ABO}:\angle\text{ACO}=1:1$
$\text{AB = AC}\Rightarrow\angle\text{ABC}=\angle\text{ACB}...(\text{i})$
In $\triangle\text{OBC},$
$\text{OB = OC} \Rightarrow\angle\text{OBC}=\angle\text{OCB}...(\text{ii})$
Subtraction (ii) from (i), we get
$\Rightarrow\angle\text{ABO}=\angle\text{ACO}$
So, $\angle\text{ABO}:\angle\text{ACO}=1:1$
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