Question

Two arcs of the same length subtend angles of 60° and 75° at the centres of the circles. What is the ratio of radii of two circles?

Answer 1

Answer:

5 : 4

Step-by-step explanation:

Let the radii of two circles be R and r

According to question

Length of Arc subtended angle 60° = Length of arc subtended angle 75°

We know that length of arc = (Ф × 2 × π × radius)/360

$\frac{60\degree \times 2 \times \pi \times R}{360\degree } = \frac{75\degree \times 2 \times \pi \times r}{360\degree }$

Multiplying both sides by 360°

               60° × 2 × π × R = 75° × 2 × π × r

Dividing both sides by 2π

                         60° × R = 75° × r

                                R/r = 75/60

                                R/r = 5/4

                              R : r = 5 : 4

∴ Ratio of the radii of both circles is 5 : 4

Answer 2

Answer:

We know that length of an arc is given by,

S = R*X , where X = angle subtended by the arc at center in degrees.

Using this,

S = A*60

S = B*75 ,

ratio of radii = A/B = 75/60 = 5/4

Step-by-step explanation:

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