A-circle-is-inscribed-in-an-isosceles-trapezium-Prove-that-the-ratio-of-the-area-of-the-circle-to-the-area-of-the-trapezium-is-equal-to-the-ratio-of-the-circum-ference-of-the-circle-to-the-perimete

Question Number 19940 by ajfour last updated on 18/Aug/17

A c i r c l e i s i n s c r i b e d i n a n

i s o s c e l e s t r a p e z i u m . P r o v e t h a t

t h e r a t i o o f t h e a r e a o f t h e c i r c l e

t o t h e a r e a o f t h e t r a p e z i u m i s

e q u a l t o t h e r a t i o o f t h e c i r c u m -

f e r e n c e o f t h e c i r c l e t o t h e

p e r i m e t e r o f t h e t r a p e z i u m .

Commented by ajfour last updated on 18/Aug/17

Commented by ajfour last updated on 18/Aug/17

A r e a o f t r a p e z i u m = 4 \times \frac{1}{2} \times R (b + a)

= R (a + b)

\frac{A r e a o f c i r c l e}{A r e a o f t r a p e z i u m} = \frac{π R^{2}}{2 R (a + b)}

= \frac{2 π R}{4 (a + b)} = \frac{P e r i m e t e r o f c i r c l e}{P e r i m e t e r o f t r a p e z i u m} .

Facebook Tweet Pin