Question

If two parallel chords of length 8 cm and 6 cm in a circle of radius 5 cm are on the opposite sides of the center then the distance between the parallel chords is

• A. $5cm$
• B. $6cm$
• C. $7cm$
• D. None of these

Answer 1

Answer: (C)

$7cm$

Let O be the center of the circle .

From O draw $OM\perp AB$ and $ON\perp CD$

In $△AOM$

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

$O{M}^2=A{O}^2-A{M}^2$

$\Rightarrow OM=\sqrt{(5{)}^2-(4{)}^2}$

$\Rightarrow OM=\sqrt{25-16}$

$\Rightarrow OM=\sqrt{9}=3cm$

In $△CON$

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

$O{N}^2=C{O}^2-C{N}^2$

$\Rightarrow ON=\sqrt{(5{)}^2-(3{)}^2}$

$\Rightarrow ON=\sqrt{25-9}$

$\Rightarrow ON=\sqrt{16}=4cm$

$\therefore MN=OM+ON=3+4=7cm$