Question

The distance of the chord of length 16 cm from the center of the circle of diameter 20 cm is

• A. 3 cm
• B. 4 cm
• C. 5 cm
• D. 6 cm

Answer 1

The correct option is D 6 cm

Let AB=16 cm is the chord of the circle with radius 10 cm

Draw $OP\perp AB$ and join BO

$PB=\frac{1}{2}AB=\frac{1}{2}\times 16=8cm$

In $△BPO\angle P={90}^{\circ }$

$\therefore O{B}^2=P{B}^2+O{P}^2$

$\Rightarrow O{P}^2=O{B}^2-P{B}^2$

$\Rightarrow OP=\sqrt{{10}^2-8^2}$

$\Rightarrow OP=\sqrt{100-64}\Rightarrow \sqrt{36}=6cm.$

Then distance of the chord from the center is 6cm.