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