If two parallel chords of a circle, having diamet

Question

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles cos-1 (1/7) and sec-1 (7) at the centre respectively, then the distance between these chords, is :	16/7	8/(71/2) 8/7	4/7

Arun · Accepted Answer

distance between chords = Radius Cos(subtended angle/2) by chord1 + Radius Cos(subtended angle/2) by chord 2 Radius = Diameter /2 = 4/2 = 2 = 2 Cos (θ₁/2) + 2Cos(θ₂/2) θ₁ = Cos⁻¹(1/7) => Cosθ₁ = 1/7 θ₂ = Sec⁻¹7 => Secθ₂ = 7 => 1/Cosθ₂ = 7 => Cosθ₂ = 1/7 Applying Cos2θ = 2Cos²θ - 1 => Cos²θ = (1 + cos2θ)/2 Putting θ = θ₁/2 Cos²(θ₁/2) = ( 1 + 1/7)/2 = 4/4 => Cos(θ₁/2) = 2/√7 Putting θ = θ₂/2 Cos²(θ₂/2) = ( 1 + 1/7)/2 = 4/7 => Cos(θ₁/2) = 2/√7 2 Cos (θ₁/2) + 2Cos(θ₂/2) = 2 *2/√7 + 2 * 2/√7 = 4/√7 + 4/√7 = 8/√7

IIT JEE Entrance Exam> If two parallel chords of a circle, havin...

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles cos^-1(1/7) and sec^-1(7) at the centre respectively, then the distance between these chords, is :

16/7

8/(7^1/2)

8/7

4/7

Prince , 8 Years ago

Arun

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IIT JEE Entrance Exam> If two parallel chords of a circle, havin...

If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the centre and subtend angles cos-1 (1/7) and sec-1 (7) at the centre respectively, then the distance between these chords, is : 16/7 8/(71/2) 8/7 4/7

Prince , 8 Years ago

Arun

LIVE ONLINE CLASSES

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