Question

The circle has radius 5cm are chord PQ of the circle is of length 8cm.find the angle the chord PQ subtends at the centre of the circle and the perimeter of the minor segment

Answer 1

Draw the radius to the ends of the chord. You have an isosceles triangle with base of 8 and sides of 5 each.
You could use the cosine law to find the central angle.
or
drop a perpendicular from the centre to the base.
You now have a right-angled triangle with a side of 4 cm and a hypotenuse of 5 cm
you can find any angle, and from there the central angle.

let me know what you get

Answer 2

Draw a diagram, as always.
If the central angle is 2θ, then
tanθ = 4/5

the perimeter is the chord + the arc subtended:
8 + 5*2θ

Answer 3

Oops. Reiny is right. sinθ = 4/5