• # question_answer Two circles with centres 0 and P, and radii 8 cm and 4 cm touch each other externally. Find the length of their common tangent QR. A)  8cm                       B)         7cm C)  $8\sqrt{2}\,cm$            D)         $7\sqrt{3}\,cm$

Join 0 to P and Q. Join P to R. Draw $\pi$. Now SP = QR, as they are opposite sides of rectangle PRQS. $\text{4}0={{\text{2}}^{\text{3}}}\times \text{5}$ $\text{6}0={{\text{2}}^{\text{2}}}\times \text{3}\times \text{5}$ $\therefore$ $={{2}^{2}}\times 3\times 5\times 2=120$ $f(p)={{\text{p}}^{\text{3}}}+\text{6}{{\text{p}}^{\text{2}}}+\text{lip}+\text{6}$ $f(p)$ $p(x)={{x}^{2}}+3x-2$