Question

two parallel chords of a circle are 12 cm and 16 cm ib length .if the diameter of the circle is 20 cm,find the distance between the parallel chords

Answer 1

I am doing it in my copy you can see the pic for your answer.

Answer 2

Distance between parallel chords is 14 cm or 2 cm.

Step-by-step explanation:

1. Given data

  Radius if circle (R)=$\frac{Diameter}{2}=\frac{20}{2}=10 cm$

  Length of one chord ($L_{1}$) =16 cm

  Length of second chord ($L_{2}$) =12 cm

2. Let perpendicular distance of chord of length 16 cm from centre of circle is $H_{1}$

   Then

$H_{1}=\sqrt{\left \{ R^{2}-\left [ \frac{L_{1}}{2} \right ]^{2} \right \}}$   ...1)

   On putting the respective value in equation 1)

$H_{1}=\sqrt{\left \{ 10^{2}-\left [ \frac{16}{2} \right ]^{2} \right \}} = 6 cm$      ...2)

3. Let perpendicular distance of chord of length 12 cm from centre of circle is $H_{2}$

    Then

$H_{2}=\sqrt{\left \{ R^{2}-\left [ \frac{L_{2}}{2} \right ]^{2} \right \}}$   ...3)

   On putting the respective value in equation 3)

$H_{2}=\sqrt{\left \{ 10^{2}-\left [ \frac{12}{2} \right ]^{2} \right \}} = 8 cm$        ...4)

5. If both is on same side with respect to centre of circle, distance between two chord

   $D_{1}=H_{2}-H_{1}=8-6=2 cm$

6. If both is on opposite side with respect to centre of circle, distance between two chord    

   $D_{2}=H_{2}+H_{1}=8+6=14 cm$