Question

Afla aria cercului galben.​

Answer 1

Afla aria cercului galben.

AB=2+4=6

AS din∆ AES dreptunghic

AS²=(2+r)²=(2-r)²+ES²

4+4r+r²=4-4r+r²+ES²

8r=ES²

ES=2√2r

BS din ∆ BGS dreptunghic

BS²=(4+r)²=(4-r)²+GS²

16+8r+r²=16-8r+r²+GS²

16r=GS²

GS=4√r

EG=AF=√6²-2²=√36-4=√32=4√2cm

ES+SG=4√2

2√2r+4√r=4√2

√r(2√2+4)=4√2 /:2

√r=2√2/(√2+2) ridicăm la pătrat

r=8/(2+4√2+4)=8/(6+4√2)=4/(3+2√2)

r=4(3-2√2)/(9-8)

r=4(3-2√2)