Circles

The circumference of a circle is the distance around the circle. It is calculated by multiplying the diameter of the circle by π.

The area of a circle is the amount of space inside the circle. It is calculated by multiplying the square of the radius of the circle by π.

The diameter of a circle is the distance across the circle through the center. It is twice the length of the radius.

The equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2.

If the radius of a circle is doubled, the circumference is also doubled.

If the radius of a circle is tripled, the area is quadrupled.

The circumference of a circle is given by C = 2πr, where r is the radius. If the circumference is 20π, then the radius is 10.

The area of a circle is given by A = πr^2, where r is the radius. If the radius is 7 cm, then the area is 147π cm^2.

The diameter of a circle is twice the length of its radius. If the diameter is 12 cm, then the radius is 6 cm.

The equation of a circle that passes through three non-collinear points can be found using the following formula: ((x - h)^2 + (y - k)^2 = r^2), where (h, k) is the center of the circle and r is the radius. Using the three given points, we can find the center and radius of the circle and then write the equation of the circle.

The area of a circle is given by (A = πr^2), where r is the radius. If the area is 36π square units, then the radius is 6 units.

The circumference of a circle is given by (C = πd), where d is the diameter. If the diameter is 14 cm, then the circumference is 22π cm.

The length of a chord that is d units away from the center of a circle with radius r is given by (\sqrt{r^2 - d^2}). If the radius is 10 cm and the chord is 8 cm away from the center, then the length of the chord is 8 cm.

The area of a sector of a circle is given by (A = \frac{θ}{360}πr^2), where θ is the central angle in degrees, r is the radius, and π is the constant pi. If the radius is 12 cm and the central angle is 60 degrees, then the area of the sector is 36π cm^2.