Quantitative Aptitude Geometry Triangles, Congruence and Similarity

In isosceles triangle PQR, PQ = PR, A and B are points on PR and PQ respectively such that AB || RQ, C and D are the points on QR such that AC || PD. If PQ = 10 cm, PA ∶ AR = 2 ∶ 3 and ∠APD = ∠BAC, then find the length of DC (in cm)

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