Question

the length of a diameter of a circle is 20cm. if the distance of a chord from the centre of the circle is 8cm, find the length of the chord.​

Answer 1

Length of Chord is 12 cm

Given Terms:

• Length of diameter of circle is 20 cm.
• Distance of chord from the centre of circle is 8 cm.

Need To Find:

• What is the length of chord ?

Solution: Assuming the length of chord to be x cm.

Radius = Diameter / 2

Radius = 20/2 = 10 cm

From attached figure we have

• OA = OB = Radius
• AB = chord
• OM = Perpendicular

In triangle AMO by using theorem of Pythagoras.

➥ AO² = AM² + MO²

➥ 10² = AM² + 8²

➥ 100 – 64 = AM²

➥ √36 = AM

➥ 6 cm = AM

Full length of chord will be 2 time of AM that is 2 × 6 = 12 cm