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Length Of Tangent

The length of a tangent is the distance between the external point from which the tangent is drawn and the point of contact on the circle. It represents the finite line segment of the tangent line that touches the circle at exactly one point.

Key Concepts

According to the Equal Tangents Theorem, the lengths of the two tangents drawn from a single external point to a circle are always equal.

The radius drawn to the point of contact is perpendicular to the tangent, creating a right-angled triangle with the center of the circle.

Because a right-angled triangle is formed, the length of the tangent can be calculated using the Pythagoras Theorem if the radius and the distance from the center to the external point are known.

Formula & Equation

Length of Tangent = √(d² - r²)

d is the distance from the center of the circle to the external point, and r is the radius of the circle.

Common Misconceptions

Myth: Students often think a tangent has an infinite length because it is a line.

Fact: While a tangent line extends infinitely in both directions, the mathematical term 'length of a tangent' specifically refers to the finite line segment between the external point and the point of contact on the circle.

Real World Applications

Calculating the line of sight distance from a satellite in space to the horizon of the Earth.

Determining the exact length of a straight road connecting a highway to the edge of a circular roundabout.

Frequently Asked Questions

How do you calculate the length of a tangent from an external point?

You can calculate it using the Pythagoras Theorem by taking the square root of the difference between the square of the distance from the center and the square of the radius.

Are the lengths of two tangents drawn from the same external point equal?

Yes, according to the Equal Tangents Theorem, two tangents drawn from a single external point to a circle are always equal in length.

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