MCQ
if $A$ and $B$ are two points on a circle such that m $(AB) = 260^\circ .$ A possible value for the angle subtended by arc $BA$ at a point on the circle is:
- ✓$50^\circ$
- B$100^\circ$
- C$75^\circ$
- D$25^\circ$
✓
Answer
Correct option: A.
$50^\circ$
We are given $m(AB) = 260^\circ $
Suppose point $P$ is on the circle.
Since $m(AB) = 260^\circ $
So, angle $AOB = 360^\circ - 260^\circ = 100^\circ $
We know that angle subtended by chord $AB$ at the centre is twice that of subtended at the point $P$
So, $\angle\text{APB}=\frac{\angle\text{AOB}}{2}=\frac{100}{2}=50^\circ$
$\Rightarrow\angle\text{APB}=50^\circ$
Suppose point $P$ is on the circle.
Since $m(AB) = 260^\circ $
So, angle $AOB = 360^\circ - 260^\circ = 100^\circ $
We know that angle subtended by chord $AB$ at the centre is twice that of subtended at the point $P$
So, $\angle\text{APB}=\frac{\angle\text{AOB}}{2}=\frac{100}{2}=50^\circ$
$\Rightarrow\angle\text{APB}=50^\circ$
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