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JEE Main20245 Apr 2024Evening ShiftMathematicsCircleActual

Let A B C D and A E F G be squares of side 4 and 2 units, respectively. The point E is on the line segment AB and the point F is on the diagonal AC . Then the radius r of the circle passing through the point F and touching the line segments BC and CD satisfies:

Options

  1. Ar=0
  2. B2 r^2-4 r+1=0
  3. C2 r^2-8 r+7=0
  4. Dr^2-8 r+8=0

Correct answer

D. r^2-8 r+8=0

Step-by-step solution

aligned & OF ^2= r ^2 & (2-r)^2+(2-r)^2= r ^2 & r ^2-8 r +8=0 aligned

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