JEE Advanced2006MathematicsCircleActual
Paragraph: Read the following passage and answer the questions. Let A B C D be a square of side length 2 units. C₂ is the circle through vertices A, B, C, D and C₁ is the circle touching all the sides of square A B C D . L is the line through A . Question: If P is a point on C₁ and Q is a point on C₂ , then P A^2+P B^2+P C^2+P D^2 Q A^2+Q B^2+Q C^2+Q D^2 is equal to
Options
- A0.75
- B1.25
- C1
- D0.5
Correct answer
A. 0.75
Step-by-step solution
Here, equation of C₂:(x-1)^2+(y-1)^2=( 2 )^2 and C₁:(x-1)^2+(y-1)^2=(1)^2 aligned & P(1+ , 1+ ) & and Q(1+ 2 , 1+ 2 ) & P A^2+P B^2+P C^2+P D^2 & = (1+ )^2+(1+ )^2 & + ( -1)^2+(1+ )^2 & + (1+ )^2+(1- )^2 & + (1- )^2+(1- )^2 & =16 & Q A^2 P A^2 = 12 16 =0.75 & aligned Hence (a) is the correct answer.