Question

What is the length of the chord whose distance from the centre is 8 cm and radius is 10 cm?

• A. 10 cm
• B. 12 cm
• C. 15 cm
• D. 18 cm

Answer 1

Answer:

B. 12 cm

According to the given question

Given:

Radius of circle = 10 cm

Distance from centre = 8 cm

Formula used:

Line perpendicular to the chord passes through the centre divide the chord into two equal areas

According to Pythagoras theorem, the sum of the square of two sides is equal to the square of the longest side

Calculation:

Let the length of chord is AB

According to Pythagoras theorem in triangle AOC

∴ (10)² = (8)² + AC²

⇒ AC² = (10)² - (8)²

⇒ AC = 6

Now, length of chord is AB = AC + BC and OC divide the chord in two equal parts

∴ AB = AC + BC = 2 $\times$ AC = 2 $\times$ 6 = 12 cm

So, the length of chord is 12 cm

Hence, option (2) is correct