The angle subtended at the circumference is half of the angle subtended at the center, so it is 120/2 = 60 degrees.

The angle subtended at the circumference is half of that at the center, so it is 80/2 = 40 degrees.

The angle subtended at any point on the remaining part of the circle is half of the angle at the center, so it is 80/2 = 40 degrees.

The angle at the circumference is half of the angle at the center, so it is 80/2 = 40 degrees.

Angle at circumference = 1/2 * angle at center = 1/2 * 80 = 40 degrees.

The angle at the circumference is half the angle at the center, so it is 80° / 2 = 40°.

The area of the sector is proportional to the central angle. 120 degrees is 1/3 of 360 degrees, hence it represents 1/3 of the circle's area.

The area of a sector is proportional to the central angle. Since 60 degrees is 1/6 of 360 degrees, the sector represents 1/6 of the circle's area.

Circumference = πd = π(10) ≈ 31.4 cm.

The radius is half of the diameter. Therefore, the radius is 10 cm / 2 = 5 cm.

Circumference = πd = π(12) = 12π cm.

The radius is half of the diameter. Therefore, the radius is 12 cm / 2 = 6 cm.

The circumference of a circle is given by C = πd. Thus, C = π(14) ≈ 43.96 cm.

The radius is half of the diameter. Therefore, the radius is 14/2 = 7 cm.

The angle θ in radians is given by the formula θ = arc length / radius. Therefore, θ = 15/10 = 1.5 radians.

The measure of the arc intercepted by an inscribed angle is twice the measure of the angle, so it is 40 * 2 = 80 degrees.

The area of a circle is given by the formula A = πr². Therefore, A = π(10)² = 100π cm².

The circumference of a circle is given by the formula C = 2πr. Thus, C = 2π(10) = 20π cm.

Diameter = 2 * radius = 2 * 10 cm = 20 cm.

The length of an arc is given by L = (θ/360) * 2πr. Here, L = (60/360) * 2π(10) = (1/6) * 20π ≈ 10.47 cm.

The length of an arc is given by the formula L = (θ/360) * 2πr. Here, L = (60/360) * 2 * π * 10 = (1/6) * 20π = 10.47 cm.

The area of a circle is given by the formula A = πr². Therefore, A = π(5)² = 25π cm².

Circumference = 2πr = 2π(5) = 10π cm.

The length of an arc is given by L = (θ/360) * 2πr. Thus, L = (60/360) * 2π(5) = (1/6) * 10π ≈ 5.24 cm.

The diameter of a circle is twice the radius. Therefore, diameter = 2 * radius = 2 * 5 cm = 10 cm.

The area of a circle is given by the formula A = πr². Therefore, A = π(7)² = 49π cm², which is approximately 154 cm².

The circumference of a circle is given by 2πr. Therefore, circumference = 2π * 7 cm = 14π cm.

The circumference of a circle is given by C = 2πr. If the radius is doubled, the new circumference is C = 2π(2r) = 4πr, which is double the original circumference.

The area of a circle is given by A = πr². If the radius is doubled, the new area becomes π(2r)² = 4πr², which is four times the original area.

Area = π * r². If radius is halved, area becomes π * (r/2)² = π * (r²/4) = (1/4) * original area.