Track quiz

Which is a piece of the circle itself? Not a region or a line.

• An arc
• A sector
• A chord

A circle has radius 26 cm and a chord 20 cm long. How far is the chord from the centre?

• 16 cm, from 26 take away 10
• 24 cm, since 676 − 100 = 576
• 10 cm, which is half the chord

Two chords sit 5 cm and 12 cm from a circle's centre. Which is longer?

• The one 12 cm out, since it reaches further
• They are equal, since the circle is the same
• The one 5 cm out, since less is taken from the radius

An arc makes 150° at the centre. What does it make at the rim?

• 300°, since the rim angle is the wider one
• 75°, since 150 ÷ 2 = 75
• 150°, since it is the same arc

P and Q both sit on chord AB's major arc. Compare angle APB with angle AQB.

• They are equal, since both halve the same centre angle
• Angle APB is bigger, since P is nearer the chord
• Angle AQB is bigger, since Q sees more of the circle

A triangle has all three corners on a circle. One side is a diameter. What is the angle opposite that side?

• About 90°, depending on the corner
• Exactly 90°, since 180 ÷ 2 = 90
• 180°, since a diameter is a straight line

A four-sided shape has all four corners on a circle. Two corners next to each other read 95° and 105°. What is the angle opposite the 95° one?

• 265°, since the two opposite ones must total 360°
• 105°, since opposite angles match
• 85°, since 180 − 95 = 85

Three points fix a circle with centre (2, 1.5) and radius 2.5. A fourth point is 2.5 from that centre. Are the four concyclic?

• Yes, since the fourth is exactly 2.5 away
• No, since four points never all fit on one circle
• There is no way to tell without drawing it

A triangle has angles of 20°, 25° and 135°. Where is its circumcentre?

• Outside the triangle, since 135° is past 90°
• Inside the triangle, since the triangle sits inside its circle
• On the middle of its shortest side

How many circles pass through two given points A and B?

• Exactly one, since two points fix the centre and the radius
• Exactly two, since the centre can be on either side of AB
• Endless, since each point on the bisector can be a centre

A regular pentagon is turned about its centre. What is the smallest turn that fits it onto itself?

• 60°, since 360 ÷ 6 = 60
• 72°, since 360 ÷ 5 = 72
• 90°, since a square fits after 90°

AB and DE are chords of one circle. Each makes 80° at the centre. AB is 12 cm. How long is DE?

• Not known, since the radius is not given
• Shorter, since DE sits lower down in the circle
• 12 cm, since equal angles give equal chords

AB makes 48° at C and 48° at D. C and D are on the same side of line AB. What follows?

• Nothing follows, since four points need not share a circle
• All four lie on one circle, since the angles are equal
• Only A, B and C share a circle, since D is new