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BITSAT2016MathematicsCircleActual

The length of the chord x+y=3 intercepted by the circle x²+y²-2 x-2 y-2=0 is

Options

  1. A7 2
  2. B3 3 2
  3. C14
  4. D7 2

Correct answer

C. 14

Step-by-step solution

The centre of the circle is ( C (1,1) ) and radius of the circle is 2 , perpendicular distance from ( C ) on ( AB ), the chord ( x + y =3 ) ( aligned & CD = | 1+1-3 2 |= 1 2 & AD = 4- 1 2 = 7 2 [ AD = AC ²- CD ² ] aligned ) Hence, the length of the chord ( AB =2 AD =2 7 2 = 14 ).

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