Question

at the centre of two circles two arcs of equal length substends at an angle of 30 and 60 respectively what is the ratio of area of two circles​

Answer 1

4 Area of small circle = Area of big circle

MEANS RATIO IS 1:4

Step-by-step explanation:

As the arch of equal length substend angles in the ratio

= 1:2

So we can say

360 ÷ 30 = 12 arcs make circumference of first circle

and

360 ÷ 60 = 6 arcs make circumference of second circle

This means the circumstances are in the ratio 2:1

Let circumference of small circle be X

circumference =

X = 2 ×pi × RS.......RS-radius small circle

and circumference of big circle will be

2X = 2 ×pi × RB.......RB-radius BIG circle

So

2 × pi × RB = 2 ( 2 × pi × RS )

= 4 × pi × RS

RB = 2 RS......................(1)

AREA = pi r square

Area of big circle = AB = pi RB ^2

Substituting from ( 1 ) we get

= pi (2RS)^2

= 4 pi RS^2............(2)

Area of small circle = AS = pi RS ^2...........(3)

from (2) and (3)

we get

4 Area of small circle = Area of big circle

MEANS RATIO IS 1:4