Constructing Tangents of a Circle

Use the navigation bar in the construction below to find out  how to construct tangents through a point in respect to a circle.

Try to redo this construction using the second applet on this page. If you need hints, use the dynamic figure above to show the construction process step by step.

Radio

y

x

z

x

y

z

r

A = (-3, 2)
B = (3, 1)
C = (1, 3)
polígono1, c, a, b = Polygon(A, B, C)
r = false
I = Incentro(polígono1)
d = OrthogonalLine(I, a)
A' = Intersect(d, a)
e = Circle(I, A')
f = OrthogonalLine(I, b)
g = OrthogonalLine(I, c)
B' = Intersect(f, b)
C' = Intersect(c, g)
h = Segment(I, A')
i = Segment(I, C')
j = Segment(I, B')
k = Segment(C, I)
l = Segment(I, B)
m = Segment(I, A)
polígono2: {Polygon[A, I, B']}
polígono3: {Polygon[C', B, I]}
polígono4: {Polygon[I, A', C]}
D = (-3.14, -1.18)
E: D + (abs(C - A'), 0.0)
F: E + (abs(B' - A), 0.0)
y0 = Segment(B', A)
x0 = Segment(A', C)
z0 = Segment(C', B)
G: F + (abs(C' - B), 0.0)
x1 = Segment(D, E)
y1 = Segment(E, F)
z1 = Segment(F, G)
H: D + (0.0, abs(A' - I))
r0 = Segment(H, D)
J: E + (0.0, abs(A' - I))
K: F + (0.0, abs(A' - I))
L: G + (0.0, abs(A' - I))
p = Segment(H, J)
q = Segment(J, K)
s = Segment(K, L)
t = Segment(L, G)
a_1 = Segment(K, F)
b_1 = Segment(J, E)
c_1 = Segment(D, J)
d_1 = Segment(E, K)
e_1 = Segment(F, L)
polígono5: {Polygon[D, H, J]}
polígono6: {Polygon[D, E, J]}
polígono7: {Polygon[E, J, K]}
polígono8: {Polygon[E, F, K]}
polígono9: {Polygon[F, K, L]}
polígono10: {Polygon[F, G, L]}

Tool: Incentro
Triángulo
Input: polígono1
Output: I

A = (-3, 2)
B = (3, 1)
C = (1, 3)
polígono1, c, a, b = Polygon(A, B, C)
d_1, e_1 = AngularBisector(b, a)
h, i = AngularBisector(c, b)
I = Intersect(e_1, i)