Triangle of Reflection

Geometry Level 3

Passing through a point A(10,12)A(10, 12), a line L1L_1 is incident on y=x3y = x\sqrt3 at point Q(x1,y1)Q(x_1, y_1). The reflected ray L2L_2 is incident on y=0y = 0 at point R(x2,y2)R(x_2, y_2). The now reflected ray L3L_3 passes through point B(103,6)B(10\sqrt3, 6). Lines L1L_1 and L3L_3 meet at point P(x3,y3)P(x_3 , y_3).

Find area of ΔPQR\Delta PQR. If area is of form ab where a,bN and b is squarefreea\sqrt{b} \text{ where } a, b\in \N \text{ and } b \text{ is squarefree} , enter answer as a+ba + b.


All of my problems are original

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