Circle Geometry

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

• The diameter is twice the radius.

• The diameter is half the radius.

• The radius is twice the diameter.

• The radius and diameter are equal.

State the tangent-secant theorem and provide an example.

• If a tangent segment is 3 units long and a secant segment is 4 units long with an external segment of 1 unit, then (3)^2 = (4)(1) which simplifies to 9 = 4, confirming the theorem.

• If a tangent segment is 4 units long and a secant segment is 6 units long with an external segment of 2 units, then (4)^2 = (6)(2) which simplifies to 16 = 12, confirming the theorem.

• If a tangent segment is 2 units long and a secant segment is 8 units long with an external segment of 4 units, then (2)^2 = (8)(4) which simplifies to 4 = 32, confirming the theorem.

• If a tangent segment is 5 units long and a secant segment is 7 units long with an external segment of 3 units, then (5)^2 = (7)(3) which simplifies to 25 = 21, confirming the theorem.

If a tangent from a point outside a circle measures 10 cm, what is the length of the tangent segment?

• 20 cm

• 15 cm

• 5 cm

• 10 cm

How do you find the length of an arc given the radius and the central angle?

• Arc Length = (Central Angle in Radians) * (Radius)

• Arc Length = (Central Angle in Radians) + (Radius)

• Arc Length = (Radius) / (Central Angle in Radians)

• Arc Length = (Central Angle in Degrees) * (Radius)

Explain how to determine the angle formed by two tangents drawn from a point outside the circle.

• The angle is equal to the diameter of the circle.

• The angle is determined by the radius drawn to the point of tangency.

• The angle is equal to the sum of the angles at the points of tangency.

• The angle formed by the two tangents is equal to half the angle subtended by the line segment connecting the points of tangency at the center of the circle.

If two chords intersect inside a circle, how do you find the lengths of the segments?

• AE + EB = CE + ED

• AE / EB = CE / ED

• AE * EB = CE * ED

• AE - EB = CE - ED

What is the formula for the area of a sector of a circle?

• A = πr²

• A = (θ/360) * π * r²

• A = (θ/180) * π * r²

• A = 2πr

Describe the properties of tangents drawn from a common external point to a circle.

• The tangents intersect at the center of the circle.

• The lengths of the tangents are equal, the angle between the tangent and the radius is 90 degrees, and the line from the external point to the center bisects the angle between the tangents.

• The lengths of the tangents are always different.

• The angle between the tangents is 180 degrees.

How do you calculate the circumference of a circle given its radius?

• C = 2 * r

• C = π * r^2

• C = π * d

• C = 2 * π * r

If the radius of a circle is doubled, how does the area change?

• The area decreases by half.

• The area increases by a factor of 2.

• The area increases by a factor of 4.

• The area remains the same.