Question

In the given figure, if $PT=\frac{16}{3}cm$ and radius of the circle is $\frac{10}{3}cm$ and PLQ and QR are tangents to circle at L and R respectively, then the length of QL is

• A. 6 cm
• B. $5\sqrt{2}$cm
• C. $6\sqrt{2}$cm
• D. 5 cm

Answer 1

The correct option is D 5 cm

Apply Tangent Secant Theorem
$P{L}^2=PT\times PR$
$P{L}^2=\frac{16}{3}\times 12=64$
[$PR=\frac{16+10+10}{3}=12$]
PL = 8 cm
Let QR = x,
QR = QL = x [ Tangents drawn from the same external point are equal to each other.]

In $\Delta QRP$,
Apply Pythagoras Theorem
$(QR{)}^2+(RP{)}^2=(PQ{)}^2$
$\Rightarrow x^2+144=(x+8{)}^2$
$\Rightarrow x^2+144=x^2+64+16x\Rightarrow x=5cm$

Hence, d is the correct option.