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NDA 2023 Maths · Mathematics · Circles · medium

The line 3x+4y=15 cuts the circle x^2+y^2=25 in a chord of length

Single correct option

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

Answer: (B) 88

The perpendicular distance of the line from the centre is 155=3\dfrac{15}{5}=3. The half-chord is 25−9=4\sqrt{25-9}=4, so the chord is 88. The value 66 doubles the distance instead of using Pythagoras, and 1010 is the diameter.
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Original question written in the NDA 2023 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