Question

in two circle , arc of equal length subtend angles of 60 degree and 75 degree at their centres, show that their radii are in the ratio 5:4

Answer 1

Answer:

Step-by-step explanation:

Let arc length of first circle be denoted as L₁ and that of second circle be denoted as L₂.

We know that Arc length of a circle is calculated as:

⇒ Arc Length = Radius × Angle subtended

⇒ L₁ = R₁ × 60° ⇒ R₁ 60 ... ( 1 )

⇒ L₂ = R₂ × 75° ⇒ R₂ 75 ... ( 2 )

We know that, L₁ = L₂

⇒ Equation ( 1 ) = Equation ( 2 )

⇒ R₁ 60 = R₂ 75

⇒ R₁ / R₂ = 75 / 60

⇒  R₁ / R₂ = 5 / 4 or 5 : 4

Hence the ratio of radius are 5 : 4.

Hence Proved !!

Hope it helped !!