$ABC$ is an isosceles triangle inscribed in a circle with centre $O$.Suppose the top vertex is $A$, the right vertex is $B$ and the left vertex is $C$. Also suppose $AC=AB$. Furthermore, the diameter $AD$ goes through $O$ and intersect $CB$ at $E$. IF $AC= \sqrt{\frac{15}{2}}$ and $OE =1$, estimate the radius of the circle.
I drew this out but cannot come up with a way to get the radius much less estimate it.
I do see similar triangles but there’s still two unknowns in the equation.
Any nudging would be appreciated.
Best Answer
Hint: use Pythagoras' theorem twice, then eliminate $\,CE\,$ between the following to find $\,r\,$:
$$ OE^2+CE^2 = r^2 \\ (OE+r)^2 + CE^2 = AC^2 $$