Question

In a circle chords $QP$ and $SR$ intersect externally at A. If $AP=7cm,PQ=14cm,AR=8cm$ then the ratio of $AR:RS$.

• A. $64:83$
• B. $83:64$
• C. $64:81$
• D. $81:64$

Answer 1

The correct option is A $64:83$

Since $QP$ and $SR$ are chords and they meet at an external point A.

$⟹QA.PA=SA.RA$

$⟹(AP+PQ).AP=AS.AR$

$AS=\frac{21\times 7}{8}=\frac{147}{8}cm$

$AR+RS=\frac{147}{8}$

$RS=\frac{147}{8}–8=\frac{83}{8}$

$\frac{AR}{RS}=\frac{8}{\frac{83}{8}}=\frac{64}{83}$