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    Question

    In the given figure, a circle is inscribed in Δ PQR,

    such that it touches the sides PQ, QR and RP at points D, E, F, respectively. If the lengths of the sides PQ = 15 cm, QR = 11 cm and RP = 13 cm, then find the length of PD.
    A 7.5 cm Correct Answer Incorrect Answer
    B 9 cm Correct Answer Incorrect Answer
    C 8.5 cm Correct Answer Incorrect Answer
    D 8 cm Correct Answer Incorrect Answer

    Solution

    A circle is inscribed in Δ PQR, such that it touches the sides PQ, QR and RP at points D, E, F, respectively. ⇒ PD = PF = x                  ⇒ QD = QE = y ⇒ RE = RF = z All are tangents. ⇒ PD + PF + QD + QE + RE + RF = PQ + QR + RP ⇒ x + x + y + y + z + z = 39 ⇒ 2x + 2(y + z) = 39 Here, y + z = QE + ER = RQ And we have RQ = 11 ⇒ 2x + 2(11) = 39 ⇒ 2x + 22 = 39 ⇒ 2x = 17 ⇒ x = 8.5 ⇒ PD = 8.5 cm

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