Answer:
The ratio of the length of DE and the length of BC = 1/4
Explanation:
From the figure we can see two sectors
To find the length of BC
The sector ABC with radius r and central angle 2β
BC = (2πr)( 2β/360)
= 4πrβ/360
To find the length of DE
The sector ADE with radius r/2 and central angle β
DE = (2πr/2)( β/360)
= πrβ/360
To find the ratio of DE to BC
DE/BC =πrβ/360 ÷ 4πrβ/360
= πrβ/360 * 360/ 4πrβ
=1/4