Question

Chords $MN$ and $RS$ of a circle intersect at $P$ outside the circle If $PN=3cm,MN=5cm,PR=2cm$ then the value of $SR$ is equal to

• A. $5cm$
• B. $8cm$
• C. $15cm$
• D. $10cm$

Answer 1

The correct option is D $10cm$

Since ,MN and RS intersect each other externally at point P

$\Rightarrow PS\times PR=PM\times PN$

$PM=PN+MN$

PN=3cm and MN=5cm

$\therefore PM=3+5=8cm$

And $PS=PR+SR$

PR=2 cm and SR=x cm

$\therefore PS=x+2$

$\Rightarrow (x+2)\times 2=8\times 3$

$\Rightarrow 2x+4=24$

$\Rightarrow 2x=24-4$

$\Rightarrow 2x=20$

$\Rightarrow x=\frac{20}{2}=10cm$

$\therefore SR=10cm$