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

Answer 1

make your sketch
join the centre to the ends of the chord.
You now have an isosceles triangle with base of 8 and sides of 5
Let the centre be C, by the cosine law:
8^2 = 5^2 + 5^2 - 2(5)(5)cosC
solve for C

The rest is easy

Answer 2

or, you have two right triangles with leg 4 and hypotenuse 5.
If the central angle subtended by the chord is 2x, then
sin x = 4/5
(From above, C = 2x)

Answer 3

We had the same question yesterday, but I can't find it.
The search does not work as nice as it used to for me.