Question-181766

Question Number 181766 by HeferH last updated on 30/Nov/22

Answered by som(math1967) last updated on 30/Nov/22

l e t r a d i u s o f i n n e r c i r c l e = r

\frac{C I}{r} = c o s e c 20 \Rightarrow C I = r c o s e c 20

c = r c o t 30 + r c o t 40

= r (\frac{c o s 30 s i n 40 + c o s 40 s i n 30}{s i n 30 s i n 40})

= r (\frac{2 s i n 70}{2 s i n 20 c o s 20})

= r [\frac{c o s (90 - 70)}{s i n 20 c o s 20}] = r c o s e c 20 = C I

∴ C I = c (p r o v e d)