In the figure, the line $BD$ is tangent to the circle at $C$. The line $AD$ passes through the centre $O$ of the circle and intersects the circle at $E$.
It is given that $\angle CDE=34^{\circ}$ and $\angle DCE=x^{\circ}$.
Find the value of $x$.
I really have no idea on how to solve this, but I have a feeling it's 26.
Triangle EOC looks like a equilateral triangle which would make DEC 120.
180 - 120 - 34 = 26.
Sorry I wasn't able to help more.
=^._.^=
Connect OC
And a radius meeting a tangent forms a 90° angle
So in triangle OCD angle DOC = 180 -90 -34 = 56°
And this equals the measure of minor arc EC
And by the tangent-chord theorem, angle DCE =(1/2) the measure of this arc =(1/2)(56) = 28°
