Circle Properties 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 a radius at the point of tangency?

Back

The tangent is perpendicular to the radius at the point of tangency.

Front

How do you find the length of a tangent segment from a point outside the circle?

Back

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

Tags

CCSS.HSG.C.A.2

Front

What is the measure of an angle formed by two tangents drawn from a point outside the circle?

Back

The measure of the angle formed by two tangents drawn from a point outside the circle is equal to half the difference of the measures of the intercepted arcs.

Tags

CCSS.HSG.C.A.2

Front

What is the formula for the circumference of a circle?

Back

The circumference C of a circle is given by the formula C = 2πr, where r is the radius.

Tags

CCSS.7.G.B.4

Front

What is the area of a circle?

Back

The area A of a circle is given by the formula A = πr², where r is the radius.

Tags

CCSS.7.G.B.4

Front

What is the relationship between the angles formed by two chords that intersect inside a circle?

Back

The measure of the angle formed by two intersecting chords is equal to the average of the measures of the arcs intercepted by the angle and its vertical angle.

Tags

CCSS.HSG.C.A.2

Front

What is the inscribed angle theorem?

Back

The inscribed angle theorem states that an angle inscribed in a circle is half the measure of the intercepted arc.

Tags

CCSS.HSG.C.A.2

Front

How do you find the length of an arc in a circle?

Back

The length of an arc can be found using the formula: Arc Length = (θ/360) × 2πr, where θ is the central angle in degrees and r is the radius.

Tags

CCSS.HSG.C.B.5

Front

What is the relationship between the central angle and the inscribed angle that subtends the same arc?

Back

The central angle is twice the measure of the inscribed angle that subtends the same arc.

Tags

CCSS.HSG.C.A.2