Unit 10 Circles: ADV Geometry Flashcards

Central Angle Formula

m∠ = measure of intercepted arc

Inscribed Angle Formula

m∠=1/2(intercepted arc)

Overlapping Arcs (Angles inside the circle)

m∠=1/2(arc1+arc2)

Degrees to Radians

radians = π/180×degrees

Radians to Degrees

degrees = 180/π×radians

Arc Length Formula

arc length=r(central angle) or arc length/circumfrance = degrees/360

Inscribed Quadrilateral

∠A+∠C=180° & ∠B+∠D=180° AND ∠A+∠B+∠C+∠D=360°

Intersecting Chords or Secants (Interior)

m∠=1/2(arc1+arc2)

Intersecting Tangents & Chords/Secants (On the Circle)

m∠=1/2(intercepted arc)

Intersecting Secants (Exterior)

m∠=1/2(large arc−small arc)

Intersecting Tangents (Exterior)

m∠=1/2(major arc−minor arc)

Area of a Circle

A=πr^2

Circumference of a Circle

C=2πr or C=πd

Equation of a Circle

(x−h)^2+(y−k)^2=r^2 ((h,k) = center and r = radius)

Chord

A line segment with endpoints on the circle.

Tangent

A line that touches the circle at exactly one point.

Secant

A line that intersects the circle in two places

Central Angle when angle = 0

Means arc length = 0

Formula to relate angle and arc length

360°=arc length/circumference

Solve for radius using the formula

arc length=degrees/360×2πr(circumference)

Congruent chords = congruent arcs (if equidistant from center)

Inscribed Angle

All three points touching the circle

If inscribed angle intercepts a diameter

It's 90°

Quadrilaterals Inscribed in Circles

Opposite angles add up to 180°

Tangent is perpendicular to the radius at the point of contact

Two tangents from the same point are

congruent

Tangent segments from a point outside the circle are

equal

For tangent-radius problems use the

Pythagorean theorem

Interior Intersection (chords)

m∠=1/2(arc1+arc2)

On Circle Intersection (tangent and chord)

m∠=1/2(intercepted arc)

Exterior Intersection (two secants, or secant + tangent)

m∠=1/2(big arc−small arc)

Standard Form

(x−h)^2+(y−k)^2=r^2

Expanded Form

x2+y2+Dx+Ey+F=0

Use Distance Formula to find radius

r=(x2−x1)^2+(y2−y1)^2 use with center and a point on the circle

Midpoint Formula

(x1+x2/2,y1+y2/2) use with endpoint of diameter the distance formul