Circles (Geo Part 2)

Front

What is the definition of a circle?

Back

A circle is the set of all points in a plane that are equidistant from a single point called the center.

Front

What is the formula to find the area of a sector of a circle?

Back

The area of a sector can be calculated using the formula: \( \text{Area} = \frac{\theta}{360} \times \pi r^2 \), where \( \theta \) is the central angle in degrees and \( r \) is the radius.

Front

If the radius of a circle is 6 inches and the central angle is 100°, what is the area of the sector in terms of \( \pi \)?

Back

The area of the sector is \( 10\pi \, \text{in}^2 \).

Front

What is a chord in a circle?

Back

A chord is a line segment whose endpoints lie on the circle.

Front

What is the relationship between the radius and the diameter of a circle?

Back

The diameter of a circle is twice the length of the radius. \( d = 2r \)

Front

What is the definition of a tangent to a circle?

Back

A tangent is a line that touches the circle at exactly one point.

Front

What is the central angle of a circle?

Back

A central angle is an angle whose vertex is at the center of the circle and whose sides are radii that extend to the circle.

Front

What is the formula for the circumference of a circle?

Back

The circumference of a circle is given by the formula: \( C = 2\pi r \), where \( r \) is the radius.

Front

What is the definition of an inscribed angle?

Back

An inscribed angle is an angle formed by two chords in a circle which have a common endpoint.

Front

How do you find the measure of an inscribed angle?

Back

The measure of an inscribed angle is half the measure of the intercepted arc.