Final answer:
A student asked about the number of different circles that can be drawn with 10 points where no 3 are collinear and 4 are concyclic. The calculation showed 21 different circles can be formed, which did not match any of the provided options, making the correct answer '(d) none of these'.
Step-by-step explanation:
The question revolves around the number of different circles that can be formed in a plane with 10 points of which no three points are collinear and 4 points are concyclic.
To find a circle, we need to choose at least 3 non-collinear points. Since 4 points are concyclic, they form a unique circle among themselves. For the remaining 6 points, we can form circles by selecting them in groups of 3.
To calculate the total number of circles: We can select 3 points from the 6 non-concyclic points in C(6,3) ways. This gives us:
C(6,3) = 6! / (3!(6-3)!) = 20
The unique circle from the concyclic points is 1. So, the total number of different circles is 20+1=21 circles. However, none of the provided options (a) 116, (b) 120, or (c) 117 matches the calculated number of circles. Therefore, the answer is (d) none of these.