Geometry Chapter 12 Formulas

Formulas for Chapter 12 (Circles)

Circumference

Distance around the circle

C = πd or 2πr

Arc Length

mARC/360° x πd (or 2πr)

Angle formed by a tangent and a chord

m∠ABC = ½ (AB)

↳ AB is an arc.

Angle formed by 2 chords

m∠ABC = ½ (AC + DB)

↳ AC and DB are arcs.

Angle formed by 2 secants, a tangent and a secant, or 2 tangents intersecting outside the circle.

m∠A = ½ (DE - BC)

↳ DE and BC are arcs.

Measure of 2 chords intersecting in a circle

(AE)(EB) = (CE)(ED)

Measure of 2 secants intersecting outside a circle

(PB)(PA) = (PD)(PC)

Measure of a tangent and a secant drawn to a circle from an external point

(PA)² = (PC)(PB)

If a center is at the origin

x² + y² = r²

If a center is not at the origin

Standard Form

(x - h)² + (y - k)² = r²

(h, k) → center of circle