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Q.

If A and B are two points on a circle such that $m (\bar{AB}) = 260^{\circ}$ find a possible value for the angle subtended by arc BA at a point on the circle

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a

100^{\circ}

b

75^{\circ}

c

50^{\circ}

d

25^{\circ}

answer is C.

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Detailed Solution

Given,
Two points on a circle = A and B
We know that
A complete circle measurement = 360°
Suppose that
On the circle point = P
Midpoint of AB,

m (arc AB) = 260^{\circ}

So,
Angle

AOB = 360^{\circ} - 260^{\circ} = 100^{\circ}

We know that,
The arc BA at a point on the circle which is angle subtended at a point P
Therefore,

∠ APB

= \frac{∠ AOB}{2}

= \frac{100}{2}

= 50^{\circ}

Hence, the required value is

50^{\circ}

.
Option 3 is correct.

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