Let C be a circle with radius 10 units and centre at the origin. Let the line x+y=2 intersects the circle C at the points P and Q . Let MN be a chord of C of length 2 unit and slope -1. Then, a distance (in units) between the chord PQ and the chord MN is

Step-by-step solution

aligned & C: x^2+y^2=10 & A N= M N 2 =1 & In O A N (O N)^2=(O A)^2+(A N)^2 & 10=(O A)^2+1 O A=3 aligned Perpendicular distance of center from PQ = |0+0-2| 2 = 2 Perpendicular distance between MN and aligned & PQ = OA + 2 or | OA - 2 | & =3+ 2 or 3- 2 aligned