SBAC Week 5 Geometry Vocabulary Circles

Find the equation of the circle with centre (3,0) and radius 6.

(x-3)²+y²=36

Find the equation of the circle with centre (6, -4) and radius 7.

(x-6)²+(y+4)²=49

What form do you usually write the equation of a circle?

(x-h)²+(y-k)²=r²

inscribed angle

2(inscribed angle) = measure of intercepted arc

Arc length= (central angle /360°) • circumference

Formula to find Arc length

Segments of Secants Theorem

If two secant segments share the same endpoint outside a circle, then the product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment (outer)(whole) = (outer)(whole)

Angles inside a circle formed by 2 chords

Sum of the intercepted arcs divided by two (average) Vertical angles = (arc1 + arc2)/2

If a quadrilateral is inscribed in a circle, the opposite angles are _____

Supplementary

The measure of an angle formed by a secant and a chord is ____ to the measure if the angle adjacent to it

Supplementary

(x+4)²+(y-1)²=25

Write the equation of this circle.

(x-5)²+(y-3)²=16

Write the equation of this circle.

Tangent

A line that intersects a circle in exactly one point

Secant

A line that intersects a circle in two points

Arc

A portion of the circumference of the circle.

Tangent Line to a Circle Theorem

A right angle is formed when a radius hits a tangent at a point of tangency

The measure of an angle formed by a tangent and a radius/diameter is _____

A right angle/90°

Chord

A segment whose endpoints are points on the circle

Concentric Circles

All the circles have the same center

Tangent and Intersecting Chord Theorem

An angle formed by a chord and a tangent that intersect on a circle is half the measure of the intercepted arc (similar to inscribed)

Central Angle

Angle whose vertex is the center of a circle

Center

Center = is equal distance from all edges of a circle

Find the centre and radius of the circle (x+5)²+(y-2)²=4

Centre (-5,2), radius 2

Find the centre and radius of the circle x²+y²+12x−8y+48=0

Centre (-6,4), radius 2

Find the centre and radius of the circle x²+18x+y²+10y+6=0

Centre (-9,-5), radius 10

Find the centre and radius of the circle (x-3)²+(y-2)²=16

Centre (3,2), radius 4

Find the centre and radius of the circle (x-8)²+(y-3)²=49

Centre (8,3), radius 7

A chord is a segment connecting two points on the _______ of a circle

Circumference

Congruent chords intercept ______ arcs

Congruent

Inscribed angles that intercept the same/congruent arc are ______

Congruent

Parallel chords intercept ______ arcs

Congruent

Two tangents drawn from the same external point are _____

Congruent

75π - 97.43 u²

Find the area of the segment. Leave your answer in terms of π (include radicals in your calculation).

16π-32 u²

Find the area of the segment. Leave your answer in terms of π.

10 u²

Find the area of the segment. Round your answer to the nearest whole number.

Measure of Major Arc

Difference between 360 and the measure of its associated minor arc

Angles outside a circle formed by 2 chords

Difference of the intercepted arcs divided by two Outside angle = (Big arc - Small arc)/2

The measure of a central angle is ____ to the measure of its intercepted arc

Equal

Congruent chord are _____ form the center of the circle

Equidistant

24 u²

Find the area of the sector

635π/9

Find the area of the sector. Leave your answer in terms of π

Arc Length D

Letter "s" used to represent arc length

The measure of an angle formed by a tangent and a chord is ____ the measure of its intercepted arc

Half

The measure of an inscribed angle is _______ the measure of its intercepted arc

Half

Semicircle

Half of a circle

Perpendicular Chord Bisector Theorem

If a radius and a chord are perpendicular then the chord and arc are bisected

Segments of Secants and Tangents Theorem

If a secant segment and a tangent share an endpoint outside a circle, then the product of the lengths of the secant segment and its external segment equals the square of the tangent segment (outer)(whole) = (outer)(whole)

Perpendicular Chord Bisector Converse

If the chord and arc are bisected then the radius or diameter and chord are perpendicular

Congruent Corresponding Chords Theorem

If two chords are congruent then their intercepted arcs are congruent

Equidistant Chords Theorem

If two chords are equidistant to the center of a circle, then they're congruent

Segments of Chords Thoerem

If two chords intersect in the interior of a circle, then the product of the lengths of the segments of the one chord is equal to the product of the lengths of the segments of the other chord (piece)(piece) = (piece)(piece)

How do you know when a point lies on the circumference of a circle?

Insert coordinates into the equation of a circle both sides of eqaution should be equal

A tangent is a line that intersects the circle ______

Once

Minor Arc

Part of the circle that measures less than 180 (use 2 letters when naming)

Major Arc

Part of the circle that measures more than 180 (use 3 letters when naming)

Inscribed / Cyclic Quadrilateral

Polygon where all of the corners are on the circle

Answer #1: about 1810 ft²

Question #1:

Answer #2: 18.9π mm²

Question #2:

Answer #3: about 14 in²

Question #3:

Answer #4: 64π in²

Question #4:

Answer #5: 135/8π in² or 16.875π in²

Question #5:

Answer #6: (4/3π − √3) m²

Question #6:

(x-1)²+(y-2)²=100

R: 10, C: (1, 2)

(x-5)²+(y-3)²=9

R: 3, C: (5,3)

(x-3)²+(y+5)²=16

R: 4, C: (3, -5)

(x+3)²+(y+5)²=25

R: 5, C: (-3, -5)

Angles inscribed in a semicircle are always _______

Right Angle/90°

How do you find the radius of a circle?

Square root the number at the end of the equation.

Diameter

The distance across a circle through its center

Radius

The distance from the center of a circle to any point on the circle

Inscribed Angle Theorem

The inscribed angle is half of the intercepted arc

Measure of Minor Arc

The measure of its central angle

Arc Measure

The measure of the center angle that intercepts the arc

Inscribed / Cyclic Quadrilateral Theorem

The opposite angles are supplementary

Point of Tangency

The point where the tangent intersects a circle

314

The radius of a circle is 10 units. What is the area? (round answer to nearest whole number)

19

The radius of a circle is 3 units. What is the circumference? (round answer to nearest whole number)

12

The radius of the circle in 6 units. What is the diameter?

External Tangent Congruence Theorem

The segments formed from a point outside a circle to the points of tangency will be congruent

Inscribed Angle

The vertex of the angle has to touch the circumference

Tangent Circles

When two circles intersect once

central angle

central angle=measure of intercepted arc

Equations for Circles

h = x-coordinate of center k = y-coordinate of center r = radius of circle

Formula of Arc Length

s=Ør