Question

in the figure,OED and OBA are sectors of a circle with centre o.find the area of the shaded region.​

Answer 1

From the given figure we have, in Δ OAB,

tanθ=

OA

AB

⇒AB=rtanθ

[Since OA=r]....(1)

And cosθ=

OB

OA

⇒OB=rsecθ.....(2).

Now PB=OB−OP=rsecθ−r......(3).[Using (2)].

Again

180

o

πθ

=

OA

AP

or,

AP

=r

180

o

πθ

........(4).

Now perimeter of the shaded region is

AB+PB+

AP

=r[secθ+tanθ+

180

o

πθ

−1]. [Using (1),(3) and (4)].