Question

Two chords AB and CD of a circle of lengths 8 cm and 6 cm respectively are parallel to each other and are on the opposite sides of its centre. If radius of the circle is 5 cm, then find the distance between AB and CD.

Answer 1

Answer:

The distance between the two chords is 7cm

Step-by-step explanation:

From the above diagram, the distance between the chords is $a+b$

From Pythagoras Theorem, $a^2+4^2=5^2$

$\Rightarrow a^2+16=25$

$\Rightarrow a^2=25-16$

$\Rightarrow a^2=9$

We take the positive square root of both sides to obtain;

$a=\sqrt{9}$

$a=3$

Also, $b^2+3^2=5^2$

$\Rightarrow b^2+9=25$

$\Rightarrow b^2=25-9$

$\Rightarrow b^2=16$

$\Rightarrow b=\sqrt{16}$

$\Rightarrow b=4$

Therefore the distance between the two chords is

$4+3=7cm$

See attachment