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พอดีว่าไปเจอโจทย์จากเพื่อนมาครับ เเละเห็นว่าสวยงามดี

Let $R$ be the point that being on the circumcircle of triangle $ABC$ such that $\hat {BCR}=\hat {RCA}=\dfrac{1}{2}\hat{ACB}$ and let $S,T$ is the mid-point of $AC,BC$ respectively. Then draw the perpendicular line to the $AC,BC$ through $S,T$ meet $CR$ at $P,Q $ respectively
Prove that the area of the following triangle are equivalent, $RPS$ and $RTQ$