Points A, B, and C are points on a circle with a radius of 6. Point D

Answer is C : Both are required and Neither alone is sufficient.

Explanation :

Consider Statement #1 : Since A, B, C can be anywhere on the circle and BD can be of any length. Therefore eliminate option A and D.
Consider Statement #2: Arc AB has length of 4\(\pi\) and we know the radius, the arc is 1/3 of the circle. But this does not solve where C lies. So Eliminate B.

Consider #1 and #2 together : Since we know arc AB is 1/3 of Circle and BD passed through point Centre and D is the midpoint of AC, then we can extend BD as diameter and can find the angle \(\angle\)ABC (which is 60 deg here). So now it becomes a right angle \(\triangle\)ABD and \(\triangle\)CBD. We can use 30-60-90 formula to calculate the Area.



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