Question

A chord of a circle is 56cm long. The distance of the chord to the centre of the circle is 20cm. a) calculate the radius of the circle b) calculate the length of a chord which is 24cm from the center of the circle.​

Answer 1

• a) 34.4 cm,
• b) 49.4 cm

Explanation:

The distance from the center to the chord is the perpendicular bisector of the chord.

The three segments form a right triangle:

• The radius - hypotenuse,
• The half-length of the chord - leg,
• The distance to the chord - another leg.

a) Use Pythagorean to find the radius:

• r² = (56/2)² + 20²
• r² = 28² + 20²
• r² = 1184
• r = √1184
• r = 34.4 cm (rounded)

b) Let the half-chord is x cm long. Use Pythagorean to find the missing leg:

• 34.4² = x² + 24²
• 1184 = x² + 576
• x² = 1184 - 576
• x² = 608
• x = √608
• x = 24.7 cm (rounded)

The length of the chord is:

• 24.7*2 = 49.4 cm