My Learning Cart
?
Categories
Account

If a chord of a circle is 16 cm long and is 6 cm away from the center, what is t

₹0.0
Login to Download
  • 📥 Instant PDF Download
  • ♾ Lifetime Access
  • 🛡 Secure & Original Content

What’s inside this PDF?

Question: If a chord of a circle is 16 cm long and is 6 cm away from the center, what is the radius of the circle?

Options:

  1. 10
  2. 12
  3. 14
  4. 16

Correct Answer: 12

Solution: 

Using the formula: radius² = (distance from center to chord)² + (half of chord length)². Here, radius² = 6² + (16/2)² = 36 + 64 = 100, so radius = √100 = 10.

If a chord of a circle is 16 cm long and is 6 cm away from the center, what is t

Practice Questions

Q1
If a chord of a circle is 16 cm long and is 6 cm away from the center, what is the radius of the circle?
  1. 10
  2. 12
  3. 14
  4. 16

Questions & Step-by-Step Solutions

If a chord of a circle is 16 cm long and is 6 cm away from the center, what is the radius of the circle?
  • Step 1: Identify the length of the chord, which is 16 cm.
  • Step 2: Identify the distance from the center of the circle to the chord, which is 6 cm.
  • Step 3: Calculate half of the chord length. Since the chord is 16 cm long, half of it is 16/2 = 8 cm.
  • Step 4: Use the formula for the radius of the circle: radius² = (distance from center to chord)² + (half of chord length)².
  • Step 5: Substitute the values into the formula: radius² = 6² + 8².
  • Step 6: Calculate 6², which is 36.
  • Step 7: Calculate 8², which is 64.
  • Step 8: Add the two results together: 36 + 64 = 100.
  • Step 9: Take the square root of 100 to find the radius: radius = √100 = 10.
  • Circle Geometry – Understanding the relationship between a chord, its distance from the center, and the radius of the circle.
  • Pythagorean Theorem – Applying the Pythagorean theorem to find the radius using the distance from the center to the chord and half the chord length.
Soulshift Feedback ×

On a scale of 0–10, how likely are you to recommend The Soulshift Academy?

Not likely Very likely
Home Practice Performance eBooks