(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

O is the centre of the circle of radius 6cm, and A and B are two points on the circumference such that angle AOB = [tex]\theta[/tex] radians.

Show that the length AB is equal to [tex]\sqrt {72 (1 - cos \theta)}[/tex]

2. Relevant equations

I think the following might be relevant:

Cosine rule: [tex]\theta = cos^-1\frac{b^2 + c^2 - a^2}{2bc}[/tex]

Area of sector = [tex]\frac{1}{2}r^2\theta[/tex]

3. The attempt at a solution

I don't really know where to start here. I think pythagoras is involved somewhere. The radius 6 must therefore be squared, multplied by 2 = 72. But I don't want to work backwards from the given soultion.

Am I missing some theory about chords of circles?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Circle question (triangles too)

**Physics Forums | Science Articles, Homework Help, Discussion**