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Incircle of a triangle: tangent lengths from the vertices

This type of question, asked 2 times: 21 Jul 2023 S1, 26 Jul 2023 S4. All 2 questions below, oldest first.

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  1. Question 1

    21 Jul 2023 S1

    67
    In the given figure, a circle is inscribed in ΔPQR\Delta PQR, such that it touches the sides PQ, QR and RP at points D, E, F, respectively. If the lengths of the sides PQ = 18 cm, QR = 13 cm and RP = 15 cm, then find the length of PD.

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  2. Question 2

    26 Jul 2023 S4

    53
    Triangle ABC is circumscribed around circle D. Segments AQ, BR and SC measure 13, 10.5 and 6 cm, respectively. The perimeter of triangle ABC is:

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