Great circles question

[mihai9]

There are three points O, P, Q, O is the center of the circle, P and Q are two points on the circle, and ∠POQ is 45 °, then it seems that the area of a triangle is 12, Find the area of a circle ?

[thucanh711]

Hi there,
hope my explanation could help you.

As O is the center of the circle and P, Q are on the circle => OP = OQ = r (the radius of the circle)

The area of the triangle can be calculated by: S = 1/2 sin($$\angle$$ POQ) OP. OQ = 1/2 . $$\frac{\sqrt{2}}{2}$$ . OP . OQ

We have S = 12 => the value of OP.OQ

OP.OQ = r. r = $$r^2$$

The area of the circle: S' = $$\pi.r^2$$

You can get your answer now.

[DrMaths]

8 of these triangles will make an octagon, whose area is 2√2r^2
So 2√2r^2 = 8 * 12
√2r^2 = 48
r^2 = 24√2

Area of circle = pi * r^2 = pi * 24√2

[treetree]

i got Pi x r ^ 2 as well!