The ratio of the length of de and the length of bc @mylittlestar

The ratio of the length of DE and the length of BC = 1/4

Step-by-step 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