Tangents of Circles

Front

What is a tangent to a circle?

Back

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

Front

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

Back

A tangent is perpendicular to the radius drawn to the point of tangency.

Front

If a line segment AB is tangent to circle C at point A, what can be said about the distance from the center of the circle to point A?

Back

The distance from the center of the circle to point A is the radius of the circle.

Front

How do you find the radius of a circle when given the length of a tangent and the distance from the center to the point of tangency?

Back

Use the Pythagorean theorem: radius^2 + tangent_length^2 = distance_from_center^2.

Front

What is the formula to calculate the length of a tangent from a point outside the circle?

Back

The length of the tangent (t) can be calculated using the formula: t = √(d^2 - r^2), where d is the distance from the point to the center of the circle and r is the radius.

Front

If the radius of a circle is 10 cm, what is the length of a tangent from a point 15 cm away from the center?

Back

Using the formula: t = √(15^2 - 10^2) = √(225 - 100) = √125 = 11.18 cm.

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 is the point where the radius is perpendicular to the tangent.

Front

Can a line be tangent to a circle at more than one point?

Back

No, a line can only be tangent to a circle at one point.

Front

What happens to the tangent line if the radius is extended beyond the point of tangency?

Back

The extended radius will intersect the tangent line at a right angle at the point of tangency.

Front

If a circle has a radius of 8 cm, what is the length of a tangent from a point 10 cm away from the center?

Back

Using the formula: t = √(10^2 - 8^2) = √(100 - 64) = √36 = 6 cm.