Question

The distance of a chord 8 cm from the centre of a circle of radius 5 cm is

• A. $4cm$
• B. $3cm$
• C. $2cm$
• D. $9cm$

Answer 1

Answer: (B)

$3cm$

Let AB =8 cm. be the chord of the circle with radius AO=5 cm.

Draw $OP\perp AB.joinOA$

according to the theorem

$AP=\frac{1}{2}AB=\frac{1}{2}\times 8=4cm.$

In $△APO,\angle A={90}^{\circ }$

$\therefore (AO{)}^2=(AP{)}^2+(OP{)}^2$

$OP=\sqrt{(AO{)}^2-(AP{)}^2}$

$\Rightarrow \sqrt{5^2-4^2}$

$\Rightarrow \sqrt{9}$

$\Rightarrow OP=3cm$