In the adjoining figure, ABC is a triangle. Through A, B and C lines are drawn parallel to BC, CA and AB respectively, which forms a triangle PQR. Show that
          2(AB + BC + CA) = PQ + QR + RP

Dear Student,

Please find below the solution to the asked query :

In quadrilateral ABPC, we have    ABCP and ACBPABPC is a gmAB = CP and BP = AC   Opposite sides of gm are equal    ....1In quadrilateral ABCR, we have    ABRC and BCARABCR is a gmAB = RC and BC = AR   Opposite sides of gm are equal    ....2from 1 and 2, we get   AB =CP = RCnow, CP = RC CP = RC = RP2so, AB = RP2    ......3Similarly, we getBC = QR2        ......4and CA = PQ2        ......5adding 3, 4 and 5, we get    AB + BC + CA = RP2+QR2+PQ22AB+BC+CA = PQ+QR+RP

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