Question

The length of a chord is 40 cm. It is 15 cm from the centre. The radius of the circle is ______.

Options

• 50 cm

• 41 cm

• 25 cm

• 30 cm

Answer 1

The length of a chord is 40 cm. It is 15 cm from the centre. The radius of the circle is 25 cm.

Explanation:

Given:

• The length of the chord = 40 cm
• The perpendicular distance from the center to the chord = 15 cm

Let the radius of the circle be r.

Now, consider a right-angled triangle formed by:

1. Half the length of the chord (since the perpendicular bisects the chord), which is 40/2 = 20 cm.
2. The distance from the center to the chord, which is 15 cm.
3. The radius, which is the hypotenuse of the triangle.

Using the Pythagorean theorem:

r² = 20² + 15²

r² = 400 + 225 = 625

r = `sqrt(625)` = 25 cm

Therefore, the radius of the circle is 25 cm.