The angle between the chords of the circle x 2 + y 2 = 100 , which passes through the point 7,1 and also divides the circumference of the circle into two arcs whose lengths are in the ratio 2 : 1 , is equal to

Step-by-step solution

Let the chord is A B which subtends an angle θ at the centre 0,0 ⇒ θ + 2 θ = 360 o ⇒ θ = 120 o = ∠ A O B Let the distance of O from A B = h Then, cos ⁡ 60 o = h 10 = 1 2 ⇒ h = 5 Let the equation of the chord is y - 1 x - 7 = m ⇒ m x - y + 1 - 7 m = 0 whose distance from 0,0 is equal to 5 ⇒ 0 - 0 + 1 - 7 m 1 + m 2 = 5 ⇒ 1 - 14 m + 49 m 2 = 25 + 25 m 2 ⇒ 24 m 2 - 14 m - 24 = 0 ⇒ m 1 m 2 = - 1 ⇒ Chords are perpendicular