![enter image source here]()
Let OO 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⇒BE=BF,andCF=CG,
As OE=OF=r, BE=BF, and OBOE=OF=r,BE=BF,andOB 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
