A chord with a length of $1$ runs from $pi/8$ to $pi/2$ radians on a circle. What is the area of the circle?

Question

1589 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-09T11:28:09

Area of the circle $= color (purple)(0.2424)$

enter image source here
Given $/_(AOB )= pi/2 - pi/8 = (3pi)/8$

$/_ (AOM) = /_ (AOB) / 2 = ((3pi)/8) / 2 = (3pi)/16$

$AB = 1, :. AM = 1/2$

Radius $OA = r = AM * sin /_AOM = (1/2) * sin ((3pi)/16)$

Radius $r = 0.2778$

$Area = pi r^2 = pi * (0.2778)^2 =0.2424$

A chord with a length of 1 1 runs from pi/8 pi/8 to pi/2 pi/2 radians on a circle. What is the area of the circle?