A circle has a radius of 10 cm. What is the length of a tangent drawn from a poi

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Question: A circle has a radius of 10 cm. What is the length of a tangent drawn from a point 15 cm away from the center?

Options:

Correct Answer: 12

Solution:

Using the tangent length formula: length = √(distance from center² - radius²) = √(15² - 10²) = √(225 - 100) = √125 = 5√5 ≈ 11.18.

A circle has a radius of 10 cm. What is the length of a tangent drawn from a point 15 cm away from the center?

A circle has a radius of 10 cm. What is the length of a tangent drawn from a point 15 cm away from the center?

Step 1: Identify the radius of the circle, which is given as 10 cm.
Step 2: Identify the distance from the point to the center of the circle, which is given as 15 cm.
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 = √(15² - 10²).
Step 5: Calculate 15², which is 225.
Step 6: Calculate 10², which is 100.
Step 7: Subtract the radius squared from the distance squared: 225 - 100 = 125.
Step 8: Take the square root of 125: √125.
Step 9: Simplify √125 to 5√5.
Step 10: If needed, approximate 5√5 to about 11.18.

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.
Pythagorean Theorem – A fundamental principle in geometry that relates the lengths of the sides of a right triangle.
Circle Properties – Understanding the properties of circles, including radius, diameter, and the relationship between a circle and tangents.