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A tangent to a circle is drawn from a point outside the circle. If the distance

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Question: A tangent to a circle is drawn from a point outside the circle. If the distance from the point to the center of the circle is 10 cm and the radius of the circle is 6 cm, what is the length of the tangent?

Options:

  1. 8 cm
  2. 10 cm
  3. 12 cm
  4. 14 cm

Correct Answer: 8 cm

Solution: 

Using the Pythagorean theorem, the length of the tangent is √(10^2 - 6^2) = √(100 - 36) = √64 = 8 cm.

A tangent to a circle is drawn from a point outside the circle. If the distance

Practice Questions

Q1
A tangent to a circle is drawn from a point outside the circle. If the distance from the point to the center of the circle is 10 cm and the radius of the circle is 6 cm, what is the length of the tangent?
  1. 8 cm
  2. 10 cm
  3. 12 cm
  4. 14 cm

Questions & Step-by-Step Solutions

A tangent to a circle is drawn from a point outside the circle. If the distance from the point to the center of the circle is 10 cm and the radius of the circle is 6 cm, what is the length of the tangent?
  • Step 1: Identify the given information. We have a point outside the circle, the distance from this point to the center of the circle is 10 cm, and the radius of the circle is 6 cm.
  • Step 2: Understand that the tangent line from the point to the circle forms a right triangle with the radius and the line from the point to the center of the circle.
  • Step 3: Label the triangle. Let 'd' be the distance from the point to the center of the circle (10 cm), 'r' be the radius of the circle (6 cm), and 't' be the length of the tangent we want to find.
  • Step 4: Use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (d) is equal to the sum of the squares of the other two sides (r and t). This can be written as: d^2 = r^2 + t^2.
  • Step 5: Substitute the known values into the equation: 10^2 = 6^2 + t^2.
  • Step 6: Calculate the squares: 100 = 36 + t^2.
  • Step 7: Rearrange the equation to solve for t^2: t^2 = 100 - 36.
  • Step 8: Calculate the right side: t^2 = 64.
  • Step 9: Take the square root of both sides to find t: t = √64.
  • Step 10: Calculate the square root: t = 8 cm.
  • Pythagorean Theorem – The relationship between the lengths of the sides of a right triangle, where the square of the hypotenuse is equal to the sum of the squares of the other two sides.
  • Tangent to a Circle – A line that touches the circle at exactly one point, forming a right angle with the radius at that point.
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