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.
- sepiaLv 73 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.
- 冷眼旁觀Lv 63 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
AB² = AD² + BD²
13² = (8 - 3)² + BD²
BD = 12
In rect. BDQR: QR = BD
Hence, QR = 12