Question

1. Explain and give the formula for the formula for the following properties for segments in a circle.

a. Segments from Chords:

b. Segments from Secants:

c. Segments from a Secant and Tangent line:

2. Explain what a radian is and how it relates to a degree.


3. Define the following terms.
a. Inscribed Circle of a Triangle:
b. Incenter:
c. Circumscribed Circle of a Triangle:
d. Circumcenter:

Answer 1

see explanation

Explanation:

1

(a)

If 2 chords of a circle intersect then the product of the measures of the parts of one chord is equal to the product of the measures of the parts of the other chord.

(b)

If 2 secants are drawn from an external point to a circle then the product of the measures of one secant's external part and the entire secant is equal to the product of the measures of the other secant's external part and that entire secant.

(c)

If a tangent and a secant are drawn from an external point to a circle , then the square of the measure of the tangent is equal to the product of the measures of the secant's external part and the entire secant.

2

A radian is defined as the angle subtended at the centre of a circle by an arc equal to the radius of the circle.

1 revolution = 360° = 2π radians

1 radian =
`(360)/(2\pi )` ≈ 57°

3

(a)

An inscribed circle of a triangle is a circle drawn inside a circle so the circle barely touches the sides of the triangle.

(b)

The incentre is at the point of intersection of the triangle's 3 angle bisectors.

(c)

A circumscribed circle of a triangle ( circles drawn around the triangle so that the circle passes through each of the triangles's vertices.

(d)

The circumcentre is at the intersection of the perpendicular bisectors of the triangle's sides.

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