TANGENTS TO A CIRCLE

TANGENTS TO A CIRCLE

tangents

Radius is perpendicular to the tangent

W can draw two tangents to a circle from a point outside the circle

The lengths of the tangents from a point to a circle are equal

Angle between the two tangents from a point outside the circle is supplementary to the angle subtended
 by the line segmnets joining points of contact at the cente

AB=√AD² +BD²

length of tangents

radius = 3 (slider from 0 to 10, step 0.5)
A = (-0.06, 5.2)
B = (6.22, 2.12)
c = Circle(A, radius)
e = true
distanceAB = Distance(A, B)
TextAB: Name[A] + (Name[B]) + " = " + distanceAB
f = Segment(A, B)
C = Midpoint(A, B)
d = Circle(C, Distance[A, C])
D = Intersect(c, d, 1)
g = Segment(D, B)
i = Segment(A, D)
E = Intersect(c, d, 2)
j = Segment(A, E)
h = Segment(B, E)
distanceAD = Distance(A, D)
TextAD: Name[A] + (Name[D]) + " = " + distanceAD
distanceDB = Distance(D, B)
TextDB: Name[D] + (Name[B]) + " = " + distanceDB
distanceAE = Distance(A, E)
TextAE: Name[A] + (Name[E]) + " = " + distanceAE
distanceEB = Distance(E, B)
TextEB: Name[E] + (Name[B]) + " = " + distanceEB
α = Angle(A, D, B)
β = Angle(B, E, A)
γ = Angle(E, A, D)
δ = Angle(D, B, E)
text4: "BD=BE=" + distanceEB + ""
text6: "∠BDA=∠BEA=" + α + ""
text8: "∠DAE + ∠EBD= " + γ + " +" + δ + "= 180⁰"
a = Distance(A, B)
text11: Name[A] + (Name[B]) + " = " + a
text9: "AB =√(" + distanceAD + ")²+(" + distanceDB + ")²=" + distanceAB + ""
b = true
k = Ray(B, D)
l = Ray(B, E)