Find the length of QR?

If the radius of circle A equals 3 and the radius of circle B equals 8 and AB=13 find the length of QR.

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  • sepia
    Lv 7
    3 weeks ago

    If the radius of circle A equals 3 and the radius of circle B equals 8 and AB = 13

    find the length of QR.

    Diagram seems to be inaccurate.

  • 3 weeks ago

    Join AQ and BR.

    It is supposed that Q and R are points of contact, and thus AQ⊥QR and BR⊥QR.

    Draw a st. line BD which⊥AQ and cuts AQ at D.

    As shown in the diagram below, BDQR is a rectangle.

    BR = DQ = 3 and BD = QR

    In ΔABD:

    AB² = AD² + BD²

    13² = (8 - 3)² + BD²

    BD = 12

    In rect. BDQR: QR = BD

    Hence, QR = 12

    Attachment image
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