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NDA 2019 Maths · Mathematics · Circles · medium

The length of the chord cut off from the circle x^2+y^2=25 by the line 3x+4y=15 is

Single correct option

The length of the chord cut off from the circle x2+y2=25x^2+y^2=25 by the line 3x+4y=153x+4y=15 is
  1. A. 88
  2. B. 66
  3. C. 44
  4. D. 1010
Show answer and solution

Answer: (A) 88

The perpendicular distance of the centre from the line is 155=3\frac{15}{5}=3. A chord at distance dd from the centre has half-length r2−d2=25−9=4\sqrt{r^2-d^2}=\sqrt{25-9}=4, so the chord is 88. The value 44 is the half-chord and 1010 is the diameter, which is the chord if the line passed through the centre.
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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