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

Question

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

TestHub · Accepted Answer

​ C : x 2 + y 2 = 10 A N = 2 MN ​ = 1 ∴ In △ O A N → ( ON ) 2 = ( O A ) 2 + ( A N ) 2 10 = ( O A ) 2 + 1 → O A = 3 ​ Perpendicular distance of center from PQ = 2 ​ ∣0 + 0 − 2∣ ​ = 2 ​ Perpendicular distance between MN and ​ PQ = OA + 2 ​ or ∣ OA − 2 ​ ∣ = 3 + 2 ​ or 3 − 2 ​ ​

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