Question

If in two circles arcs of the same length subtend angles of 45 degree and 90 degree at the centre find the ratio of their radii

answer ​

Answer 1

$\large\underline\pink{Given:-}$

• In two circle arcs of the same length subtend angle to 45 degree and 90 degree at the centre.

$\large\underline\pink{To find:-}$

• Fine the ratio of radius of circle ....?

$\large\underline\pink{Solutions:-}$

• let length of two circle be l

Angle subtend at centre are:-

⟹ 45° = 45 × π/180 radian

⟹ 45° = π/4 radian

⟹ 90° = 90 × π/180 radian

⟹ 90° = π/2 radian

theta = length of arc / radian of circle be r1 and R2

• Radius of 1st circle = r1 = 1/π / 4

⟹ r1 = 1 × 4/π

⟹ r1 = 4l/π

• Radius of 2nd circle = r2 = 1/π / 4

2

⟹ r2 = 1 × 2/π

⟹ r2 = 2l/π

• Ratio of the radian of the circle

⟹ 4l/π / 2l/π

⟹ 4l/π × π/2l

⟹ 4l/2l

⟹ 2/1

hence, the ratio of radian of circle 2:1