Solution:
Let \(O\) be the circumcenter of \((A B C)\) . Let \(M\) , \(N\) , and \(L\) be the midpoints of \(O D\) , \(P C\) , and \(Q B\) respectively.

Claim 1. \(\triangle O P Q\) and \(\triangle D C B\) are directly similar.

Proof. Clearly \(D B = D C\) and \(O Q = O P\) . Also note that \(\angle Q O P = 2\angle Q D P = 2\angle Q D A + 2\angle P D A =\) \(\angle B D A + \angle C D A = \angle B D C\) . So the two triangles are directly similar by SAS.

Claim 2. \(M L = M N\) and \(\angle L M N = 180^{\circ} - \angle B A C\)

Proof. Note that since \(\triangle O Q P\sim \triangle D B C\) by the Mean Geometry Theorem, we have that the average of the two triangles is also similar to them, therefore \(\triangle M L N\sim \triangle D B C\Rightarrow M L = M N\) and \(\angle L M N =\) \(\angle B D C = 180^{\circ} - \angle B A C\)

Let \(K\) be the reflection of \(A\) over \(M\)

Claim 3. \(K\) is the circumcenter of \(\triangle R T S\)

Proof. Note that since \(A Q R B\) and \(A P S C\) are parallelograms we have that \(A - L - R\) are collinear and that \(A - N - S\) are collinear. The homothety centered at \(A\) with scale- factor 2 maps \(\triangle L M N\) to \(\triangle R K S\) , therefore \(K R = K S\) and \(\angle R K S = \angle L M N = \angle B D C = 2(180^{\circ} - \angle R T S)\) (and \(K\) and \(T\) are in opposite sides of \(R S\) ), implying that \(K\) is the circumcenter of \(\triangle R T S\)

Claim 4. \(K T = K I\)

Proof. Note that \(A O K D\) is a parallelogram. Let \(B T\) intersect the \((A B C)\) again at point \(G\) . Since \(\angle A B G = \angle A B T = \angle Q A B = \angle Q C A\Rightarrow A Q = A G\) and also \(O Q = O G\) hence \(A O\perp Q G\) . Then by Reim's theorem we have that \(Q G\parallel T I\) and also that \(A O\parallel D K\) , so \(D K\perp T I\) . Since \(D I = D T\) , it means that \(K D\) is the perpendicular bisector of \(T I\) , therefore \(K T = K I\) .

This means that \(R T I S\) is cyclic with center \(K\) .

Remark. When \(K\) and \(T\) are on the same side of \(R S\) , it can be shown that \(\angle R K S = 2\angle R T S\) .

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Let \(A B C\) be an acute triangle with incentre \(I\) and \(A B \neq A C\) . Let lines \(B I\) and \(C I\) intersect the circumcircle of \(A B C\) at \(P \neq B\) and \(Q \neq C\) , respectively. Consider points \(R\) and \(S\) such that \(A Q R B\) and \(A C S P\) are parallelograms (with \(A Q \parallel R B\) , \(A B \parallel Q R\) , \(A C \parallel S P\) , and \(A P \parallel C S\) ). Let \(T\) be the point of intersection of lines \(R B\) and \(S C\) . Prove that points \(R\) , \(S\) , \(T\) , and \(I\) are concyclic.

Solution:
As shown above, we have that \(BTIC\) is cyclic. Let \(D\) and \(E\) be the second intersections of \(AC\) and \(AB\) with this circle, respectively. Since the center of this circle lies on \(AI\) (by symmetry about \(AI\) ), we have that \(AB = AD\) and \(AC = AE\) , therefore \(BE = CD\) . Note that since \(C - I - Q\) and \(A - B - E\) are collinear, by Reim's theorem we have that \(AQ \parallel EI\) and since \(AQ \parallel BT\) , we have that \(BT \parallel EI\) . Similarly, we get \(CT \parallel DI\) . Let \(F\) and \(G\) be the intersections of \(ID\) and \(IE\) with \(PS\) and \(QR\) , respectively. Clearly, \(RGEB\) and \(FSCD\) are parallelograms. Since \(RGEB\) is parallelogram and \(BEIT\) is isosceles trapezoid, we have that \(RGIT\) is isosceles trapezoid. Similarly, \(SFIT\) is isosceles trapezoid. Hence, both of them are cyclic. Note also that \(QR = AB = AD = PF\) and \(QG = AE = AC = PS\) . Since \(QR\) and \(PS\) are tangents to the circumcircle of \(\triangle ABC\) we have that \(R\) and \(F\) are symmetric (reflections) about the perpendicular bisector of \(PQ\) . Similarly, \(G\) and \(S\) are symmetric about the perpendicular bisector of \(PQ\) . This gives us that \(QP \parallel RF \parallel GS\) and that \(RFSG\) is an isosceles trapezoid, hence a cyclic quadrilateral with \(\angle RGS = 180^{\circ} - \angle GQP = 180^{\circ} - \angle QAP = 180^{\circ} - \angle RTS \Rightarrow R, G, S, T\) are concyclic. Combining all the facts about the cyclic quadrilaterals we proved above, we have that \(R, G, S, F, I, T\) are concyclic. Therefore \(R, T, I, S\) lie on a circle.

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