Question

Please solve q 116 ?

Answer 1

`(3) 75pi " cm"^2`

Explanation:

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`