Question

the perimeter of the sector is equal to half of the circumference of a circle. find the measure of the angle of the sector at the centre of radian​

Answer 1

Answer:

Let α be the angle of sector of radius r then according to the given condition, we have

perimeter of sector of radius  r=length of arc of semi-circle of radius  r

rα+2r=πr

α+2=π

α=π−2 (radians)

=65.40844097383535∘

Step-by-step explanation:

Answer 2

Answer:

Step-by-step explanation:

Let r be the radius of a circle. Perimeter of a sector = half of the   circumference ∴ l(OA) + l(OB) + l(arc APB) = 1 2 (2πr) ∴ r + r + r.θ    = πr  2r + r.θ  = πr ∴ 2 + θ = π ∴ θ = (π − 2)c