Question

How to calculate one side of a triangle?

I have a circle with the radius of 8.0 cm. Inside the circle I have a triangle drawn like the image. I know that the shortest distance from the mid point in the circle to x is 2 cm. How do I calculate x?

Answer 1

`4sqrt15`

Explanation:

The line `x` is a chord and the line from the centre, that is length
2 cm, bisects the chord and meets it at `90^@`. Using the 2 cm line, a radius as the hypotenuse and half the line `x` we can form a right angled triangle. If we call this missing length `l` we can find it using Pythagoras : `8^2-2^2= l^2`
`64-4=l^2, l=sqrt60=2sqrt15`

This length is half `x` so `x=2xx2sqrt15=4sqrt15`