Question

In a circle the length of each of two
parallel chords is 16 cm. If the diameter
of the circle is 20 cm, find the distance
between the chords.​

Answer 1

Answer

12 cm

Explanation

Refer the attachment for figure.

Given that the lengths of two chords (say AB and CD) is 16 cm and they are parallel to each other. The diameter of circle = 20 cm ⇒ radius = 10 cm

We know that equal chords are equidistant from the centre of the circle. So, if one chord is located at a distance of x cm from the centre, the other chord would be located at a distance of x too. Hence, the distance between them would be 2x cm.

Now, let the distance between a chord and the centre of circle be x. So, the perpendicular OM is of length x. We know that the perpendicular from centre bisects the chord. Hence, in ΔOMB, MB = 8 cm

Apply Pythagoras theorem

OM² + MB² = OB²

⇒ x² + 8² = r²

⇒ x² + 8² = 10² (r = 10 cm)

⇒ x² = 10² - 8²

⇒ x² = 100 - 64

⇒ x² = 36

⇒ x = 6 cm

So, the distance between two chords = 2x = 2 × 6 = 12 cm.

Answer 2

Answer:

Step-by-step explanation:

given d=20cm , r=10

length of the chord is 16, when we draw a line from center of the circle to the chord it will bisect the into two halves

so v can construct a triangle with h=10cm , a=8cm \sqrt{10^{2} -8^{2} } \\

=6CM(DISTANCE FROM CENTER TO CHORD)

SO 6+6=12 CM