Unit Eight Geometry FULL

Question 1

Circle

Answer 1

A set of points equidistant from a given point (centre)

Question 2

Radius

Answer 2

A segment with endpoints at the centre and on the circle

Question 3

Chord

Answer 3

A segment with endpoints on the circle but not specifically collinear with the centre

Chords are congruent if:
* They are equidistant from center
* They for corresponding arcs
(if AB=CD, then ⌒AB=⌒CD)
If a diameter or radius is perpendicular to a chord, it bisects the chord and its arc

Question 4

Diameter

Answer 4

A chord collinear with the centre, and twice the radius (d=2r)

Question 5

Secant

Answer 5

A line that intersects the circle at two points and possibly extends. Can be a chord.

Question 6

Tangent

Answer 6

A line that touches the circle at only one point. A line is tangent to a circle only if it is perpendicular to a radius (making it a right angle) and drawn to a point of tangency.

If:
* Two segments from the same external point are tangent, they are congruent
* A polygon is circumscribed (drawn around), all sides are congruent

Question 7

Segment Lengths

Answer 7

Three types: intersecting interior chords/secants (type 1), intersecting exterior secants (type 2), and an intersecting exterior secant and tangent (type 3).

Type 1: ab=cd
Type 2: a(a+b)=c(c+d)
Type 3: a²=b(b+c)

Question 8

Point of Tangency

Answer 8

Where the tangent hits the circle

Question 9

Central Angle

Answer 9

One vertex at the centre, the sides are radii (and thus equal). The central angle is equal to the arc. In specific problems, the central angle can be posed as “angle of rotation.” They are the same thing.

∠ABC=⌒AC

Question 10

Intersections

Answer 10

Occurring within the circle and outside the circle, any angle that is not a central or inscribed angle. The three types are interior, on-the-circle, and exterior

Note: if two tangents create an exterior intersection, the angle and the closest arc add to 180.

• If two chords intersect, ½(intercepted arc+opposite arc)
• If a secant and a tangent intersect at a point of tangency, ½(intercepted arc)
• If secants or tangents intersect outside of the point of tangency, ½(furthest arc - closest arc)

Question 11

Inscribed Angle

Answer 11

Angle with a vertex on the circle and chords for sides

∠ABC=½⌒AC
* If an inscribed angle is on a diameter, it is a right angle.
* If two inscribed angles are on the same arc, the angles are equal.
(∠ABC=∠ADC)

Question 12

Inscribed Quadrilateral

Answer 12

A quadrilateral with each vertex on the circle

If a quadrilateral is inscribed in a circle, then its opposite angles are supplementary.

Question 13

Arc

Answer 13

A portion of the edge of the circle defined by two endpoints.

Question 14

Minor Arc

Answer 14

Arc with a measure under 180, always indicated by a two letter arc. E.g., ⌒AB

Question 15

Major Arc

Answer 15

Arc with a measure greater than 180 and 3 letters to name it. E.g., ⌒ABC

Question 16

Semicircle

Answer 16

An arc with a measure of 180 with points on the diameter.

Question 17

Area

Answer 17

πr²

Question 18

Circumference

Answer 18

2πr or πd

Question 19

Arc Length

Answer 19

(central angle/360) · 2πr

Question 20

Sector Area

Answer 20

(central angle/360) · πr²