Let #O# be the center of the circle.
Recall that tangent segments to circle from an external point are equal in length,
#=> BE=BF, and CF=CG#,
As #OE=OF=r, BE=BF, and OB# is common hypotenuse,
#=> DeltaOBE and DeltaOBF# are congruent,
let #angleBOE=x, => angleBOF=x#,
similarly, as #OF=OG=r, CF=CG and OC# is common hypotenuse,
#=> DeltaCOF and DeltaCOG# are congruent,
let #angleCOF=y, => angleCOG=y#,
Now, as #angleEOG=180^@, => 2(x+y)=180^@#.
#=> x+y=90^@#
#=> angleOCG=90-y=x#
#=> DeltaCOG and DeltaOBE# are similar,
#=> (BE)/(OE)=(OG)/(CG)#,
#=> 5/r=r/15#
#=> color(red)(r^2=75)#
area of the circle #= pi*r^2=75pi " cm"^2#
