Question

The distance between two parallel chords of lengths 8 cm and 6cm in a circle of diameter 10 cm if the chords are on the same side of the center is

• A. 1 cm
• B. 2 cm
• C. 3 cm
• D. 4 cm

Answer 1

The correct option is A 1 cm

Let AB=8 cm is the chord of the circle with radius 5 cm

Draw $OP\perp AB$ and join BO

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

In $△BPO\angle P={90}^{\circ }$

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

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

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

$\Rightarrow OP=\sqrt{25-16}\Rightarrow \sqrt{9}=3cm.$

Let CD=6 cm is the chord of the circle with radius 5 cm

Draw $OQ\perp CD$ and join DO

$QD=\frac{1}{2}CD=\frac{1}{2}\times 6=3cm$

In $△QDO\angle Q={90}^{\circ }$

$\therefore O{D}^2=Q{D}^2+O{Q}^2$

$\Rightarrow O{Q}^2=O{D}^2-Q{D}^2$

$\Rightarrow OQ=\sqrt{5^2-3^2}$

$\Rightarrow OQ=\sqrt{25-9}\Rightarrow \sqrt{16}=4cm.$

$PQ=OQ-OP=4-3=1cm$