# Circle theorems

```The angle at the centre of a circle is twice the
angle at the circumference of the circle from
the same arc.
The angle formed in a semicircle is always a
right angle.
Angles from the same arc in the same segment
are equal.
to 180O. a+c=180, b+d=180
The perpendicular line from the centre of a
circle to a chord, bisects the chord.
The angle between a tangent and the radius, at
the point where the tangent touches the circle,
is a right angle.
Two tangents drawn from a point to a circle are
equal.
The angle between a tangent and a chord is equal
to the angle at the circumference in the
alternate segment.
b
a
a
b
Sheet 1:
a = 44&deg;, b = 31&deg;, c = 90&deg;,
d = 90&deg;, e = 90&deg;, f = 90&deg;,
h = 95&deg;, i = 103&deg;, j = 26&deg;,
k = 33&deg;, m = 97&deg;, n = 84&deg;, p = 94&deg;,
q = 86&deg;, r = 106&deg;, s = 43&deg;,
t = 86&deg;,
x = 74&deg;,
g = 98&deg;,
u = 37&deg;, v = 37&deg;, w = 37&deg;,
y = 53&deg;,
Sheet 2:
a = 21&deg;, b = 90&deg;, c = 90&deg;,
d = 108&deg;, e = 71&deg;, f = 68&deg;,
h = 110&deg;, i = 110&deg;, j = 56&deg;,
k = 35&deg;, m = 92&deg;, n = 34&deg;, p = 68&deg;,
q = 12&deg;, r = 71&deg;,
t = 38&deg;,
s = 38&deg;,
g = 70&deg;,
u = 109&deg;, v = 77&deg;, w = 110&deg;,
x = 62&deg;,
Sheet 3:
a = 59&deg;, b = 74&deg;, c = 5 cm, d = 90&deg;, e = 5 cm, f = 35&deg;,
h = 74&deg;, i = 27&deg;,
q = 30&deg;, r = 109&deg;,
j = 67&deg;,
k = 6&deg;,
g = 61&deg;,
m = 44&deg;, n = 136&deg;, p = 109&deg;,
```