Question

The number of circles that can be drawn out of $10$ points of which $7$ are collinear, is

• A. $85$
• B. $130$
• C. $45$
• D. $5040$

Answer 1

The correct option is A $85$

A unique circle can be drawn from three non-collinear points

(1) Two points from collinear and one from non-collinear is ${}^7{C}_2\times {}^3{C}_1=63$

(2) One point from collinear and two from non collinear is ${}^7{C}_1\times {}^3{C}_2=21$

(3) Three non-collinear points is ${}^3{C}_3=1$

Then, the total number of circles drawn $=63+21+1=85$.