Question

In Fig., two circles intersect each other at points $P$ and $Q$. From $A$ on line $PQ$, secant $AMD$ for one circle and secant $ASR$ for the second one are drawn. If $AM=3,MD=5$ and $AS=4$, determine $SR$.

• A. $2$ cm
• B. $4$ cm
• C. $3$ cm
• D. $1$ cm

Answer 1

The correct option is A $2$ cm

In the large circle, chord QP and chord DM intersect each other at the point A outside the circle
$\therefore AM\times AD=AP\times AQ$ .....(1)
Again in the smaller circle, chord QP and chord RS intersect each other at the point A outside the circle.
$\therefore AS\times AR=AP\times AQ$ ...(2)
[From (1) and (2)]

$\therefore AM\times AD=AS\times AR$ .....(3)
Now AD =AM +MD
= 3 + 5 = 8

From (3), $3\times 8=4\times AR$
$\Rightarrow AR=\frac{24}{4}=6$
But AS + SR = AR
$\therefore$ 4 + SR = 6
SR = 6 - 4 = 2