Question 84
In the triangle $ABC$ $\angle A=75^\circ$ and $\angle C=45^\circ$. Points $P$ and $T$ are chosen on the segments $AB$ and $BC$ in such a way that quadrilateral $APTC$ is cyclic and $CT = 2AP$. Point $O$ is the circumcenter of $\triangle ABC$. The ray $TO$ crosses side $AC$ in a point $K$. Prove that $TO=OK$.
(Anton Trygub)
Editorial note: the source refers to Figure 30, but no corresponding image is supplied; the construction and proof are specified in the text.
(Anton Trygub)
Editorial note: the source refers to Figure 30, but no corresponding image is supplied; the construction and proof are specified in the text.