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In a plane the circles \mathcal K_1 and \mathcal K_2 with centers I_1 and I_2, respectively, intersect in two points A and B. Assume that \angle I_1AI_2 is obtuse. The tangent to \mathcal K_1 in A intersects \mathcal K_2 again in C and the tangent to \mathcal K_2 in A intersects \mathcal K_1 again in D. Let \mathcal K_3 be the circumcircle of the triangle BCD. Let E be the midpoint of that arc CD of \mathcal K_3 that contains B. The lines AC and AD intersect \mathcal K_3 again in K and L, respectively. Prove that the line AE is perpendicular to KL.

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