# Finding the radius with chord length

I'm struggling to find the radius of the circle in the image (the only other given length is the length between B and the right angle below, which is 5). Is it even possible to get the radius without knowing any other dimensions? Or is there a way to find it? I've tried to use Pythagoras but without knowing the length of the side of the triangle going towards O, it was hard to find it.

• Where have the 2.8s come from in your diagram? – mrnovice Feb 23 '17 at 22:00
• It was given in the problem, where they asked to get the angle that I marked as theta. – Estermont Feb 23 '17 at 22:05
• Just to clarify then, everything in the diagram you provided is from the question itself? – mrnovice Feb 23 '17 at 22:05
• Yes I think so.The only information that I didn't put was 5 m (between point B and the right angle below it). – Estermont Feb 23 '17 at 22:09
• Well I'm almost done, just need to find the angle PBO, if you have any ideas – mrnovice Feb 23 '17 at 22:22

There is no way to find $\theta$ or the radius from the given data. To see why, imagine to move point $P$ to the left on the horizontal line and let $O$ be the center of circle $ABP$: all given lengths would stay the same, but $r$ and $\theta$ would change.
• Thank you for reminding me of that.The angle of course is maximum when the radius is minimum, that is when the circle is tangent to the base line ($r=7,8$ m). – Aretino Feb 25 '17 at 8:52
• Sorry, I should have written $r=7.8$ m. That is: when the circle is tangent, the radius is equal to the distance of $O$ from the baseline. – Aretino Feb 25 '17 at 12:43