Question

What is the ratio of the length of DE to the length of BC ?

Answer 1

Look at the picture.

$CB=\dfrac{2\beta}{180^o}\cdot\pi r=\dfrac{\pi r\beta}{90^o}\\\\DE=\dfrac{\beta}{180^o}\cdot \pi\cdot\dfrac{r}{2}=\dfrac{\pi r\beta}{360^o}\\\\\dfrac{DE}{BC}=DE:BC=\dfrac{\pi r\beta}{360^o}:\dfrac{\pi r\beta}{90^o}=\dfrac{\pi r\beta}{360^o}\cdot\dfrac{90^o}{\pi r\beta}=\boxed{\dfrac{1}{4}}$

Answer: A. 1/4