By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 2 2024 Maths, question 37

Topic: Algebra

Q37

What is the maximum number of possible points of intersection of four straight lines and a circle (intersection is between lines as well as circle and lines)?

  1. (a) 66
  2. (b) 1010
  3. (c) 1414Correct answer
  4. (d) 1616

Solution.

Answer: (c) 1414

  1. Four lines give at most C(4,2)=6 distinct mutual intersections.
  2. Each line meets a circle at at most two points, adding 8.
  3. By avoiding parallel lines, triple concurrence, tangency and coincident intersections, all 6+8=14 can be distinct.