If a circle has a radius of 5 units, what is the length of a tangent drawn from

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Question: If a circle has a radius of 5 units, what is the length of a tangent drawn from a point 13 units away from the center?

Options:

Correct Answer: 10

Solution:

Using the tangent length formula: length = √(distance from center² - radius²) = √(13² - 5²) = √(169 - 25) = √144 = 12.

If a circle has a radius of 5 units, what is the length of a tangent drawn from a point 13 units away from the center?

If a circle has a radius of 5 units, what is the length of a tangent drawn from a point 13 units away from the center?

Step 1: Identify the radius of the circle, which is given as 5 units.
Step 2: Identify the distance from the point to the center of the circle, which is given as 13 units.
Step 3: Use the formula for the length of the tangent: length = √(distance from center² - radius²).
Step 4: Substitute the values into the formula: length = √(13² - 5²).
Step 5: Calculate 13², which is 169.
Step 6: Calculate 5², which is 25.
Step 7: Subtract the radius squared from the distance squared: 169 - 25 = 144.
Step 8: Take the square root of 144: √144 = 12.
Step 9: Conclude that the length of the tangent is 12 units.

Tangent Length Formula – The formula for finding the length of a tangent from a point outside a circle, which is derived from the Pythagorean theorem.
Circle Geometry – Understanding the properties of circles, including radius, center, and the relationship between tangents and radii.