Author: BV

Class 9-Circles-Arc Degree Measure Theorem

Use slider α to change ∠AOB and 
slider “Radius”for changing the radius
of the circle.After that click the button 
“StartANimation”. Stop and Refresh buttons 
can also be used if needed

AIM: To verify arc degree measure theorem

AIM

How to proceed ?

Start Animation

Stop Animation

Benny Varghese
PGT Maths
JNV Pathanamthitta
Kerala-686511

SPECIAL CASES

Spl Case One

Spl Case Two

Refresh

c = Circle(A_1, B_1)
D = Point(c)
b = Ray(D, B_1)
e = Segment(A_1, B_1)
E = Point(c)
f = Circle(E, 4)
O = (6.266666666666667, -0.03333333333333333)
Radius: 5.4
g = Circle(O, Radius)
C = Point(g)
B = Point(g)
i = Ray(C, B)
k = Segment(O, B)
F = Point(i)
u = Vector(C, F)
α: 120°
A = Rotate(B, α, O)
β = Angle(B, O, A)
h = Segment(O, A)
O_1 = (10.338802083333333, -0.9050781249999991)
g_1 = Circle(O_1, Radius)
C_1 = Point(g_1)
k_1 = Segment(O_1, C_1)
O_2 = (12.74359375, -0.6221614583333328)
g_2 = Circle(O_2, Radius)
C_2 = Point(g_2)
k_2 = Segment(O_2, C_2)
j = Line(C, A)
G = Point(j)
v = Vector(C, G)
l = AngularBisector(B, O, A)
m = Line(C, k)
A_2 = Point(l)
ε = Angle(B, O, A_2)
H = Intersect(m, l)
I = Point(l)
ζ = Angle(C, H, I)
J = Point(u)
K = Point(m)
η = Angle(K, C, J)
d = Circle(O, 1.5)
L = Intersect(d, k)
M, N = Intersect(d, l)
a: -1.5
B_3 = Dilate(O, If[1 < a < 2, 2 - a, 0], C)
w_1 = Vector(O, B_3)
p = CircleSector(O, L, N)
q = Translate(p, w_1)
q' = Rotate(q, If[2 < a < 3, ((a - 2) * η), η], C)
P = Intersect(d, h)
r = CircleSector(O, N, P)
s = Rotate(r, If[-1 < a < 0, ((-(a + 1)) * ε), (-ε)], O)
s' = Rotate(s, If[0 < a < 1, (a * ε), ε], O)
n = false
o: false
t = false
w: false
γ = Angle(B, C, A)