Question 1135825




first find the angle subtended at the center by the chord, we will have to use the Cosine Rule 

 {{{A=cos^-1((b^2+c^2-a^2)/2bc)}}}

{{{b=c=radius=10cm}}}

{{{a=chord_ length=12cm}}}

{{{A}}}=angle subtended at center of circle


{{{ A=cos^-1((10^2+10^2-12^2)/(2*10*10))}}}

{{{A=cos^-1((100+100-144)/200)}}}

{{{A=cos^-1(56/200)}}}

{{{A=cos^-1(0.28)}}}

{{{A=73.74}}}°



{{{Area=(1/2)*r^2((2pi*A)/360-sin(A))}}}

{{{Area=(1/2)*10^2((2*3.14*73.74)/360-sin(73.74))}}}

{{{Area=(1/2)*100(1.2863533-0.960001)}}}

{{{Area=(1/2)*32.63523}}}

{{{Area=16.32cm^2}}}