Find the length of QR?

Question

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

Answer 1

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.

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Answer 2

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

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