A-square-whose-area-is-s-2-contains-a-semicircle-of-possible-largest-area-Determine-radius-of-the-semicircle-

Question Number 3836 by Rasheed Soomro last updated on 22/Dec/15

A s q u a r e, w h o s e a r e a i s s^{2}, c o n t a i n s

a s e m i c i r c l e o f p o s s i b l e l a r g e s t a r e a .

D e t e r m i n e r a d i u s o f t h e s e m i c i r c l e .

Commented by Yozzii last updated on 24/Dec/15

r = \frac{s}{2} . I t h i n k t h a t i n o r d e r t o

o b t a i n a s e m i - c i r c l e o f l a r g e s t a r e a

i n a s q u a r e, i t i s n e c e s s a r y t h a t i t s

s t r a i g h t e d g e i s p a r a l l e l t o o n e o f t h e

s i d e s o f t h e s q u a r e . I f a n y l a r g e r s i d e l e n g t h

i s s o u g h t a f t e r, p a r t o f t h e s e m i c i r c l e

l i e s o u t s i d e t h e s q u a r e . I n o t h e r w o r d s,

i f t h e a r m r e p r e s e n t i n g t h e s i d e e d g e o f t h e s e m i c i r c l e i s

f r e e t o r o t a t e θ ° w i t h i n t h e r e g i o n o f t h e

s q u a r e a b o u t o n e o f t h e c o r n e r s o f t h e

s q u a r e (θ = a n g l e b e t w e e n a r m a n d s i d e o f s q u a r e), o n l y w h e n θ = 0 ° c a n w e

c o m p l e t e l y c o n t a i n a s e m i - c i r c l e i n

t h e f i x e d s q u a r e . S o s = 2 r \Rightarrow r = \frac{s}{2} .

Commented by RasheedSindhi last updated on 24/Dec/15

S t r a i g h t e d g e o f s e m i c i r c l e i s p a r a l l e l t o o n e

o f t h e d i a g o n a l s o f t h e s q u a r e a n d

i t t o u c h e s a l l t h e s i d e s o f s q u a r e .

Commented by RasheedSindhi last updated on 24/Dec/15

D r a w i n g a s e m i c i r c l e (b y r u l e r

a n d c o m p a s s) i n a s q u a r e t h a t

t o u c h e s a l l t h e s i d e s o f t h e

s q u a r e i s a f a m i l i a r c o n s t r u c t i o n

p r o b l e m .

Commented by Yozzii last updated on 24/Dec/15

H m m . O k .

Commented by Rasheed Soomro last updated on 29/Dec/15