Tangent lines with circles

Front

What is a tangent line to a circle?

Back

A tangent line is a straight line that touches a circle at exactly one point, known as the point of tangency.

Front

What is the relationship between a radius and a tangent line at the point of tangency?

Back

The radius drawn to the point of tangency is perpendicular to the tangent line.

Front

If a point is outside a circle, how can you find the length of the tangent from that point to the circle?

Back

Use the Pythagorean theorem: if the distance from the point to the center of the circle is 'd' and the radius is 'r', then the length of the tangent 't' is given by t = √(d² - r²).

Front

What is the formula for the length of a tangent segment from a point outside the circle?

Back

Length of tangent = √(distance from point to center² - radius²).

Front

If AB is a tangent to the circle at point A, and OA is the radius, what can be said about angles OAB and OBA?

Back

Angles OAB and OBA are complementary, meaning they add up to 90 degrees.

Front

How do you find the radius of a circle if you know the length of the tangent and the distance from the center to the external point?

Back

Use the formula: radius = √(distance² - tangent length²).

Front

What is the significance of the point of tangency in relation to the circle?

Back

The point of tangency is the only point where the tangent line touches the circle, and it defines the direction of the tangent line.

Front

What is the perimeter of a circle segment formed by two tangent lines?

Back

The perimeter is the sum of the lengths of the two tangent segments and the arc between the points of tangency.

Front

If two tangent segments are drawn from a single external point to a circle, what can be said about their lengths?

Back

The lengths of the two tangent segments are equal.

Front

What is the relationship between the angles formed by two intersecting tangents at a point outside the circle?

Back

The angle formed by the two tangents is equal to half the difference of the measures of the intercepted arcs.