FLASHCARD - Arc Length, Area of Sector, Intersecting Chords & Secant

Front

What is the formula for arc length?

Back

Arc Length = (θ/360) * 2πr, where θ is the central angle in degrees and r is the radius.

Front

Define the area of a sector of a circle.

Back

Area of Sector = (θ/360) * πr², where θ is the central angle in degrees and r is the radius.

Front

What is the relationship between intersecting chords in a circle?

Back

If two chords intersect inside a circle, the products of the lengths of the segments of each chord are equal: (a * b) = (c * d).

Front

How do you calculate the area of a sector given the radius and central angle?

Back

Use the formula: Area = (θ/360) * πr².

Front

What is the formula for the length of an arc in a circle?

Back

Arc Length = (θ/360) * 2πr.

Front

If the radius of a circle is 10 cm and the central angle is 60°, what is the area of the sector?

Back

Area = (60/360) * π(10)² = (1/6) * 100π ≈ 52.36 cm².

Front

What is the formula for the area of a circle?

Back

Area = πr², where r is the radius.

Front

How do you find the length of a bold arc if the radius is 5 ft and the central angle is 90°?

Back

Arc Length = (90/360) * 2π(5) = (1/4) * 10π ≈ 7.85 ft.

Front

What is the significance of the central angle in calculating arc length?

Back

The central angle determines the proportion of the circle that the arc represents.

Front

If two secants intersect outside a circle, what is the relationship between the segments?

Back

If two secants intersect outside a circle, the product of the lengths of one secant and its external segment equals the product of the lengths of the other secant and its external segment.