Question

In the circular lawn, there is a $16$ m long path in the form of a chord. If the path is $6$ m away from the centre of the lawn, then the radius of the circular lawn is

• A. $16$ m
• B. $6$ m
• C. $10$ m
• D. $8$ m

Answer 1

Answer: (C)

$10$ m

Given that chord length $\left(AB\right)$ is $16$ cm

A perpendicular $OC$ is drawn from center $O$ to the chord $AB$, where $C$ is the foot of perpendicular on $AB$

$OC\perp AC,$
$\Rightarrow AC=CB$
$\Rightarrow AC=\frac{16}{2}=8$

In $\Delta OAC$, using pythagoras theorem

$O{A}^2=A{C}^2+O{C}^2$
$\Rightarrow O{A}^2=8^2+6^2=100$
$\Rightarrow OA=10$ m
$\therefore$ radius of the circular lawn $=10$ m.

Hence, option C is correct.