Question

The diameter of a circle is 30 cm. If length of one chord is 20 cm, then distance of chord from center will be:

• A. $5\sqrt{5}cm$
• B. $5cm$
• C. $3\sqrt{5}cM$
• D. $2\sqrt{5}cm$

Answer 1

Answer: (A)

$5\sqrt{5}cm$

Diameter of circle = $30cm$
Radius of circle $=\frac{30}{2}=15cm$
$AP=PB=\frac{20}{2}=10cm[\because OP\perp AB]$
In right angled $\Delta OPB$
$O{B}^2=O{P}^2+P{B}^2$
${15}^2=O{P}^2+{10}^2$
$225=O{P}^2+100$
$O{P}^2=125$
$OP=\sqrt{125}$
$OP=5\sqrt{5}cm$
Thus, (A) is correct.