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.
Opposite angles of a cyclic quadrilateral add up
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
Answers:
Sheet 1:
a = 44°, b = 31°, c = 90°,
d = 90°, e = 90°, f = 90°,
h = 95°, i = 103°, j = 26°,
k = 33°, m = 97°, n = 84°, p = 94°,
q = 86°, r = 106°, s = 43°,
t = 86°,
x = 74°,
g = 98°,
u = 37°, v = 37°, w = 37°,
y = 53°,
Sheet 2:
a = 21°, b = 90°, c = 90°,
d = 108°, e = 71°, f = 68°,
h = 110°, i = 110°, j = 56°,
k = 35°, m = 92°, n = 34°, p = 68°,
q = 12°, r = 71°,
t = 38°,
s = 38°,
g = 70°,
u = 109°, v = 77°, w = 110°,
x = 62°,
Sheet 3:
a = 59°, b = 74°, c = 5 cm, d = 90°, e = 5 cm, f = 35°,
h = 74°, i = 27°,
q = 30°, r = 109°,
j = 67°,
k = 6°,
g = 61°,
m = 44°, n = 136°, p = 109°,