Question

The diameter of a circle is 100 cm. The length of a chord is 60 cm. The distance of the chord from the centre is ______.

Options

• 80 cm

• 60 cm

• 50 cm

• 40 cm

Answer 1

The diameter of a circle is 100 cm. The length of a chord is 60 cm. The distance of the chord from the centre is 40 cm.

Explanation:

Step 1: Calculate the radius of the circle.

The radius r is half the diameter.

`r = "diameter"/2`

`r = (100  cm)/2`

r = 50 cm

Step 2: Calculate half the length of the chord.

The perpendicular from the center bisects the chord.

Half-chord length `l_("half") = "chord length"/2`

`l_("half") = (60  cm)/2`

`l_("half")` = 30 cm

Step 3: Use the Pythagorean theorem to find the distance.

Let d be the distance from the center to the chord.

The radius, half-chord and distance form a right-angled triangle.

r² = d² + l²_half

50² = d² + 30²

2500 = d² + 900

d² = 2500 – 900

d² = 1600

d = `sqrt(1600)`

d = 40 cm

The distance of the chord from the center is 40 cm.