Find the length of the chord in the circumference

Question

In the figure, $OP=8$, $PQ=12$, then $QR=?$

I don't know how to use the angles, i tried to do some equilateral triangles, but got nothing there.

Any hints?

By observation, i think the lenght of $QR$ might be $20$, but i don't know how to get to that result.

Answer 1

HINT

Apply trig Cosine Rule twice, noting the isoscles triangle $OQR$ in order to find $r$ at first and then to find $ QR.$

Answer 2

Assuming that $O$ is the centre of the circle, the cosine rule applied to $OP$ and $PQ$ will give the radius $OQ$, and hence also $OR$. Extend $PO$ until it intersects $RQ$ at $S$ to form an equilateral triangle. You now know two sides $OS$, $OR$ and the angle $OSR$, so can calculate $RS$ using the sine rule.