Tangents of Circles Review

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.

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, what can be said about the distance from the center of the circle to the line segment?

Back

The distance from the center of the circle to the line segment is equal to the radius of the circle.

Front

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

Back

The length of the tangent segment can be found using the formula: length = √(d² - r²), where d is the distance from the point to the center of the circle and r is the radius.

Front

If two tangents 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 measure of the angle formed between a tangent and a chord through the point of tangency?

Back

The measure of the angle formed is equal to the measure of the opposite angle formed by the chord.

Front

How do you find the perimeter of a figure that includes tangents and arcs?

Back

To find the perimeter, add the lengths of the tangent segments and the lengths of the arcs.

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 touches the circle.

Front

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

Back

Using the formula, length = √(15² - 10²) = √(225 - 100) = √125 = 5√5.

Front

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

Back

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