1. Symmetry in Circles
Isosceles triangles have two equal sides and two equal angles. e° f° b°
30° n°
e = (180 – 30)°  2 m° a°
70°
= 75°
110°
a = 70°
f = e = 75°
b = 180 – 70 – 70
= 40°
m = 180 –110 = 70°
n = 180 –
= 40°

2. Isosceles Triangles & Circles
If we draw a triangle inside a circle using radii then it will be isosceles because it has two equal sides.
Ex1
Ex2 v° w° c° b° a°
12° f° e°
a = 12°
e° = f°
b = 180 – 12 – 12
= 156°
v° = w°
c = 180 – 156
= 24°

3. Ex3
p = 65° t°
q = 180 – 65 – 65
= 50°
120° r°
r = 360 – 120 – 50
= 190° q° s° p°
s = (180 – 120)  2
= 30°
65°
t = s = 30°

4. So the large triangle is right-angled.
Ex4
a = (180 – 40)  2
= 70°
b = a = 70° e° c°
40°
c = 180 – 40
= 140° a° d° b°
d = (180 – 140)  2
= 20°
e = d = 20°
NB: b + d =
= 90°
So the large triangle is right-angled.