Question

A chord is 3cm from the centre of a circle of radius 14cm. Calculate the angle subtended by the chord and the circumference of the circle?

Answer 1

This is a drawing of, `color(red)("the circle"), color(blue)("the chord"), color(green)("the distance") and color(orange)("the two radii that subtend the angle")`

The line from the center to the chord bisects the subtended angle `theta`, therefore, we write the equation:

`cos(theta/2) = (3" cm")/(14" cm")`

`theta = 2cos^-1(3/14)`

`theta ~~ 2.71" radians"`

The circumference is `C = 2pir`:

`C = 2pi(14" cm")`

`C = 28pi" cm"`