Date: 12 Leden 2013

$\text{1) 2 libovolné sečny}$

\text{2) tětivy}

$α$

$α$

$\text{3) Obvodové úhly příslušné k témuž oblouku AD → oba α}$

$γ$

$\text{3) Obvodové úhly příslušné k témuž oblouku AD → oba α$

$\text{3) Obvodové úhly příslušné k témuž oblouku AD → oba α$

$\text{3) Obvodové úhly příslušné k témuž oblouku AD → oba α$

4) \text{ }\Delta MBD∼\Delta MCA⇒\frac{|MA|}{|MC| }=\frac{|MD| }{|MB|}⇒| MA|·|MB|=|MD|·|MC|

S = (0, 5)
B_1 = (0, -5)
c = Circle(S, B_1)
M = (20, 10)
B = Point(c)
a = Line(B, M)
A = Intersect(c, a, 2)
d = Circle(A, M)
h = OrthogonalLine(B, a)
b = OrthogonalLine(M, a)
e = Circle(M, A)
C_1 = Intersect(e, b, 2)
g = OrthogonalLine(C_1, b)
D_1 = Intersect(h, g)
C = Point(c)
D_2 = Line(M, C)
E, D = Intersect(c, D_2)
f = Segment(C, A)
i = Segment(D, B)
P = Intersect(f, i)
α = Angle(D, B, A)
β = Angle(D, C, A)
k = CircleArc(S, D, A)
γ = Angle(B, M, C)

Tool: Chordála
2 kružnice
Input: c, d
Output: h

a, b, e, f = Tangent(c, d)
A, B_1 = Intersect(c, b)
B = Intersect(d, b)
C = Midpoint(A, B)
D = Center(c)
E = Center(d)
g = Segment(D, E)
h = OrthogonalLine(C, g)