Question

There are $10$ points in a plane of which no three are collinear and some four points are concylic . The maximum number of circles that can be drawn using these is:

• A. $116$
• B. $120$
• C. $117$
• D. $110$

Answer 1

Answer: (C)

$117$

$10$ points of which $4$ points are concyclic:

$6C_3+6C_{1}4C_2+6C_{2}4C_1+1$

$=\frac{6\times 5\times 4}{6}+6\times \frac{4\times 3}{2}+\frac{6\times 5}{2}\times 4+1$

$=20+36+60+1$

$=117$ .