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Questions and Answers
Write an equation of a circle with a center at $(-7, 1)$ and radius $r = 7$.
Write an equation of a circle with a center at $(-7, 1)$ and radius $r = 7$.
$(x+7)^2 + (y-1)^2 = 49$
Name three points that lie on the circle defined by the equation $(x+7)^2 + (y-1)^2 = 49$.
Name three points that lie on the circle defined by the equation $(x+7)^2 + (y-1)^2 = 49$.
Examples: $(-7, 8)$, $(0, 1)$, $(-14, 1)$, $(-7, -6)$. (Any point satisfying the equation is correct).
Given Circle C with diameter RU, find the measure of arc ST (mST).
Given Circle C with diameter RU, find the measure of arc ST (mST).
$75^\circ$
Given Circle C with diameter RU, find the measure of arc QUS (mQUS).
Given Circle C with diameter RU, find the measure of arc QUS (mQUS).
Find the value of x in the diagram where two chords intersect inside the circle.
Find the value of x in the diagram where two chords intersect inside the circle.
Given Circle C, find the value of x.
Given Circle C, find the value of x.
Given Circle C, find the value of y.
Given Circle C, find the value of y.
Find the value of x in the diagram where an angle is formed by two secants intersecting outside the circle.
Find the value of x in the diagram where an angle is formed by two secants intersecting outside the circle.
Given: AE = 8, AH = 7, ES = y, and HL = y + 3. Find the value of y using the intersecting secants theorem.
Given: AE = 8, AH = 7, ES = y, and HL = y + 3. Find the value of y using the intersecting secants theorem.
In Circle G, $mArc(KV) = (7x)^\circ$, $mArc(SK) = (5x + 55)^\circ$, $mArc(VS) = 65^\circ$. Find the measure of arc SK (mSK).
In Circle G, $mArc(KV) = (7x)^\circ$, $mArc(SK) = (5x + 55)^\circ$, $mArc(VS) = 65^\circ$. Find the measure of arc SK (mSK).
Given the $mArc(CJM) = (5x + 20)^\circ$ and $m\angle CMN = 115^\circ$, find the value of x.
Given the $mArc(CJM) = (5x + 20)^\circ$ and $m\angle CMN = 115^\circ$, find the value of x.
Using the diagram where two secants intersect outside the circle, find the value of x.
Using the diagram where two secants intersect outside the circle, find the value of x.
Write the equation of a circle with diameter endpoints A(3,0) and B(7,6).
Write the equation of a circle with diameter endpoints A(3,0) and B(7,6).
In diagram 9a, find the value of x, representing the measure of arc AB assuming central angle AOB=96.
In diagram 9a, find the value of x, representing the measure of arc AB assuming central angle AOB=96.
In diagram 9a, find the value of z, representing an angle in the isosceles triangle OAE, assuming arc AE is $96^\circ$.
In diagram 9a, find the value of z, representing an angle in the isosceles triangle OAE, assuming arc AE is $96^\circ$.
Using the calculation $x = (96-24)/2$ based on diagram 9b where 96 and 24 represent intercepted arcs, find the value of x.
Using the calculation $x = (96-24)/2$ based on diagram 9b where 96 and 24 represent intercepted arcs, find the value of x.
Using the calculation $y = (96+24)/2$ based on diagram 9b where 96 and 24 represent intercepted arcs, find the value of y.
Using the calculation $y = (96+24)/2$ based on diagram 9b where 96 and 24 represent intercepted arcs, find the value of y.
Using the calculation $z = 96/2$ based on diagram 9b where 96 represents an intercepted arc, find the value of z.
Using the calculation $z = 96/2$ based on diagram 9b where 96 represents an intercepted arc, find the value of z.
What is the perimeter of $ riangle ABC$, given that segments AB, BC, and CA are tangent to Circle O?
What is the perimeter of $ riangle ABC$, given that segments AB, BC, and CA are tangent to Circle O?
Given $OB = \sqrt{28}$, what is the radius of Circle O?
Given $OB = \sqrt{28}$, what is the radius of Circle O?
What is the value of x (the central angle) in the diagram for question 10?
What is the value of x (the central angle) in the diagram for question 10?
Given Circle C with radius 6 and $m\angle ACB = 100^\circ$, find the length of arc AB. Simplify your answer and leave it in terms of $\pi$.
Given Circle C with radius 6 and $m\angle ACB = 100^\circ$, find the length of arc AB. Simplify your answer and leave it in terms of $\pi$.
In a circle whose radius is 6 in., the area of a sector is $15\pi$ in$^2$. Find the measure of the central angle of the sector.
In a circle whose radius is 6 in., the area of a sector is $15\pi$ in$^2$. Find the measure of the central angle of the sector.
Find the area of the shaded region, assuming it is a circular segment defined by a $90^\circ$ central angle in a circle with radius 8 cm (based on calculation notes).
Find the area of the shaded region, assuming it is a circular segment defined by a $90^\circ$ central angle in a circle with radius 8 cm (based on calculation notes).
In diagram 14, find the value of angle a.
In diagram 14, find the value of angle a.
In diagram 14, find the value of angle b.
In diagram 14, find the value of angle b.
In diagram 14, find the value of angle c.
In diagram 14, find the value of angle c.
In diagram 14, find the value of angle d.
In diagram 14, find the value of angle d.
In diagram 15, where l1 and l2 are tangents, find the value of angle b.
In diagram 15, where l1 and l2 are tangents, find the value of angle b.
In diagram 15, find the value of angle c.
In diagram 15, find the value of angle c.
In diagram 15, find the value of angle d.
In diagram 15, find the value of angle d.
In diagram 15, find the value of angle e.
In diagram 15, find the value of angle e.
In diagram 15, find the value of angle f.
In diagram 15, find the value of angle f.
In diagram 15, find the value of angle g.
In diagram 15, find the value of angle g.
Solve for x using the intersecting secants theorem and the quadratic formula, based on the diagram in question 16.
Solve for x using the intersecting secants theorem and the quadratic formula, based on the diagram in question 16.
Solve for x using the tangent-secant theorem based on the diagram in question 18.
Solve for x using the tangent-secant theorem based on the diagram in question 18.
Flashcards
Inscribed Angle
Inscribed Angle
An angle whose vertex is on the circle and whose sides are chords of the circle.
Semicircle
Semicircle
Half of a circle, an arc whose measure is 180 degrees.
Tangent
Tangent
A line that touches a circle at only one point.
Secant
Secant
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Chord
Chord
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Minor Arc
Minor Arc
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Major Arc
Major Arc
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Diameter
Diameter
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Intercepted Arc
Intercepted Arc
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Central Angle
Central Angle
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(x-h)^2+ (y-k)^2=r^2
(x-h)^2+ (y-k)^2=r^2
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Study Notes
Circle Parts
- ∠FDB is an inscribed angle.
- DFB is a semicircle.
- AH is a tangent.
- CG is a secant.
- DF is a chord.
- EG is a minor arc.
- FEG is a major arc.
- DB is a diameter.
- FB is an intercepted arc.
- ∠JPB is a central angle.
Equation of a Circle
- The equation of a circle with a center at (-7, 1) and a radius of 7 is (x+7)² + (y-1)² = 49.
Circle Measurements
- Given circle C with diameter RU, if m arc ST = 75°, then m arc QUS = 270°.
- x = 68
- In circle O, if arc y = 133° then x = 47 and y = 133°.
- x = 50
- If AE = 8, AH = 7, ES = y, and HL = y + 3, then y = 6.
Arcs and Angles in a Circle
- In circle G, if m arc KV = (7x)°, m arc SK = (5x + 55)°, and m arc VS = 65°, then x = 20 and m arc SK = 155°.
- Given m arc CJM = (5x + 20)° and m∠CMN = 115°, then x = 42.
- (2x-1) (4) = (x-2)(x+7), x = 5
Equation of a Circle with Given Diameter
- For a circle with diameter AB where A(3,0) and B(7,6), the center is (5,3).
- The equation of the circle is (x-5)² + (y-3)² = 13.
Circle Angles
- If FA and ET are not diameters of circle O, then x = 96°, y = 96°, and z = 42°.
- Given x = 36, y = 60 and z = 48
Tangent and Perimeter Calculations
- If AB, BC, and CA are tangent to circle O, the perimeter of triangle ABC is 20 units.
- If OB = √28 = 2√7, the radius is √3.
- The value of x in the quadrilateral is 120°.
- The length of arc AB in circle C is (10/3)π units when the measure of arc AB is 100° and the radius is 6.
Area of a Sector
- Given radius is 6, the measure of the central angle of the sector is 150° when the area of the sector is 15π.
Area of Shaded Region
- The area of the shaded region is approximately 18.3 units².
Circle Variables
- a = 90°
- b = 90°
- c = 70°
- d = 65°
- b = 90°
- d = 70°
- e = 48°
- f = 132°
- c = 42°
- g = 50°
Solving for Variables
- 3x(3x+4x) = (3x+1)(3x+1+2x+1), x = 2
- AC and DB are diameters of circle J, AE ≅ CE ≅ DE ≅ EB, ∠AED ≅ ∠BEC. Hence, triangles ΔEAD ≅ ΔECB by SAS.
- Tangent = secant, x = 6 units
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