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NDA 2019 Maths · Mathematics · Circles · medium

A tangent to a circle is perpendicular to the radius drawn to its point of contact. 2. The line y=x+3 touches the circle x^2+y^2=9.

Single correct option

Consider the following statements:
1. A tangent to a circle is perpendicular to the radius drawn to its point of contact.
2. The line y=x+3y=x+3 touches the circle x2+y2=9x^2+y^2=9.
Which of the statements given above is/are correct?
  1. A. 1 only
  2. B. 2 only
  3. C. Both 1 and 2
  4. D. Neither 1 nor 2
Show answer and solution

Answer: (A) 1 only

Statement 1 is a standard theorem and is true. For statement 2, the distance of the centre (0,0)(0,0) from x−y+3=0x-y+3=0 is 32≈2.12\frac{3}{\sqrt2}\approx2.12, which is less than the radius 33, so the line cuts the circle at two points and is not a tangent. Only statement 1 is correct.
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Original question written in the NDA 2019 Maths pattern and checked twice for the correct answer. Not an official question paper. How we write and check questions · Corrections policy · Report a mistake