Circles Study Guide Flashcards

A set of flashcards covering circle formulas including circumference, area, arc length, sector area, shaded segments, tangent lines, and chord properties.

What is the formula for the circumference of a circle?

$$C = 2\pi r$$

What is the formula for the area of a circle?

$$A = \pi r^2$$

What is the formula for calculating Arc Length?

$$\frac{\text{degree of arc}}{360} \times 2\pi r$$

Based on the notes, what is the exact Arc Length for a circle with a radius of $4$ and an arc of $70^{\circ}$?

$$\frac{14}{9}\pi$$

What is the formula for the Area of a Sector?

$$\frac{\text{degree of arc}}{360} \times \pi r^2$$

How is the Area of a Shaded Segment calculated?

$$\text{Area of sector} - \text{Area of triangle}$$

In the example for the Area of a Shaded Segment with a radius of $10$ and an arc of $36^{\circ}$, what is the calculated Area of the Sector?

$$10\pi$$

According to section 10-2, what is the geometric relationship between a tangent line and a radius at the point of tangency?

They are perpendicular, forming a $90^{\circ}$ angle.

According to section 10-3, if the distances from the center to two chords are equal ($OM = OE$), what can be concluded about chords $AB$ and $CD$?

$$AB = CD$$

In the triangle calculation provided in section 10-3, what is the value of the hypotenuse $c$ when the legs are $30$ and $6$?

$$c \approx 30.59$$