Angles at the Centre
100: The angle at the centre is ______ the angle at the circumference.
Twice as big.
Angles in the same segment are always…
Equal.
The angle in a semicircle is always…
90°.
Opposite angles in a cyclic quadrilateral add up to…
180°.
: A radius is always ______ to a tangent at the point of contact.
Perpendicular (90°).
If the angle at the circumference is 35°, what is the angle at the centre?
A: 70°.
A chord subtends a 40° angle at one point on the circumference. What’s the angle at another point in the same segment?
40°.
A triangle drawn with one side as the diameter is always what type of triangle?
Right-angled triangle.
If one angle in a cyclic quadrilateral is 110°, what is the opposite angle?
70°.
Tangents from an external point are always…
Equal in length.
: If the angle at the centre is 120°, what is the angle at the circumference?
A: 60°.
True or False: Angles in the same segment can be different sizes.
A: False.
True or False: The size of the semicircle changes the angle.
False.
True or False: All four angles in a cyclic quadrilateral add to 360°.
True.
The angle between a tangent and a chord equals the angle in the ______ segment.
Alternate segment.
Angles in the same segment are always
Equal.
A chord subtends an angle of 65° in one segment. What is the angle in the opposite segment?
A: 115° (since together they make 180°).
A diameter subtends an angle at the circumference. What is the angle?
A: 90°.
In a cyclic quadrilateral, one angle is 95°. What is the opposite angle?
85°.
Two tangents are drawn from an external point to a circle. One is 7 cm. What is the other?
7 cm.
True or False: The angle at the centre is always smaller than the angle at the circumference.
False.
State the theorem that describes angles subtended by the same chord in the same segment.
Angles in the same segment are equal.
Explain why a triangle with one side as the diameter is always right-angled.
A: Because the angle in a semicircle is 90°.
State the theorem for opposite angles in a cyclic quadrilateral.
They add up to 180°.
State the theorem about perpendicular bisectors of chords.
The perpendicular bisector of a chord passes through the centre of the circle.