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NDA 2021 Maths · Mathematics · Circles · medium

The length of the chord intercepted on the x-axis by the circle (x-3)^2+(y-4)^2=25 is

Single correct option

The length of the chord intercepted on the xx-axis by the circle (x−3)2+(y−4)2=25(x-3)^2+(y-4)^2=25 is
  1. A. 88
  2. B. 1010
  3. C. 33
  4. D. 66
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Answer: (D) 66

Put y=0y=0: (x−3)2=25−16=9(x-3)^2=25-16=9, so x=0x=0 or x=6x=6. The chord from (0,0)(0,0) to (6,0)(6,0) has length 66. Equivalently 2r2−d2=225−16=62\sqrt{r^2-d^2}=2\sqrt{25-16}=6 where d=4d=4 is the distance of the centre from the axis.
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Original question written in the NDA 2021 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