Checkpoint: diameters, cyclic shapes and finding a centre

A straight stick crosses a round plate through its centre. Both ends touch the rim. A dot on the rim is joined to both ends. What angle is made at the dot?

• 90°, since 180 ÷ 2 = 90
• 180°, since the stick is a straight line
• It depends on where the dot is put

A cyclic quadrilateral has an angle of 118°. What is the angle opposite it?

• There is not enough information to say
• 242°, since the two must total 360°
• 62°, since 180 − 118 = 62

A circle through three points has centre (2, 1.5) and radius 2.5. A fourth point sits 2.9 away from that centre. Are all four concyclic?

• No, since 2.9 is not 2.5
• Yes, since 2.9 is close to 2.5
• Yes, since every four points lie on some circle

Where is the circumcentre of a right-angled triangle?

• At the corner that holds the right angle of the triangle
• At the middle of the side opposite the right angle
• At the middle of one of the two shorter sides

A triangle has an angle of 130°. What can be said about its circumcentre?

• It sits inside the triangle, since the triangle sits inside the circle
• It sits on the longest side of the triangle
• It sits outside the triangle, since 130° is past 90°