MCQ
If $A$ and $B$ are two points on a circle such that $\text{m}\big(\widehat{\text{AB}}\big)=260^\circ.$ A possible value for the angle subtended by arc $BA$ at a point on the circle is:
- A$100^\circ$
- B$75^\circ$
- ✓$50^\circ$
- D$25^\circ$
✓
Answer
Correct option: C.
$50^\circ$
$\text{m}\big(\widehat{\text{AB}}\big)=260^\circ$
$\Rightarrow\text{m}\big(\widehat{\text{BA}}\big)=100^\circ$
Now Let $\widehat{\text{BA}}$ subtend an angle $\theta$ at a point $C$ on circle.
Now, we know that angle subtend by an arc at the center is double the angle subtended at any point on the circle.
$\Rightarrow100^\circ=2\theta$
$\Rightarrow\theta=50^\circ$
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