Maths

Question 1

If AM = MB, what is the theorem

Answer 1

If a line drawn from the centre of a circle is perpendicular to a chord, then it bisects the chord.

Question 2

If OM is perpendicular to AB, what is the theorem?

Answer 2

If a line drawn from the centre of a circle bisects the chord, then it is perpendicular to the chord.

Question 3

If O is the centre of a circle, what is the theorem?

Answer 3

If a line is a perpendicular bisector of a chord, then it passes through the centre of the chord.

Question 4

If O ₁ = 2C, what is the theorem?

Answer 4

The angle subtended by an arc at the centre of a circle is double the size of the angle subtended by the same arc at the circumference.

Question 5

If C is a right angle, what is the theorem?

Answer 5

If an angle is subtended by the diameter at the circumference of the circle, then its magnitude is 90°.

Question 6

If AB is the diameter of a circle, what is the theorem?

Answer 6

If the angle subtended by a chord at the circumference of the circle is 90°, then the chord is a diameter.

Question 7

If A = B and C = D, what is the theorem?

Answer 7

If angles are subtended by the same chord on the same side of the circle, then they are equal.

Question 8

If ABCD is a cyclic quadrilateral, what is the theorem?

Answer 8

If a line segment subtends equal angles at 2 points on the same side of the line segment, then the 4 points are concyclic.

Question 9

If A = B, what is the theorem?

Answer 9

If chords are equal, then they subtend equal angles at the circumference of the circle.

Question 10

If O₁ = O₂, what is the theorem?

Answer 10

If chords are equal, then they subtend equal angles at the centre of the circle.

Question 11

If AB = DE, what is the theorem

Answer 11

If angles are equal at the circumference or the centre, they are subtended by equal chords.

Question 12

If P + R = S + Q = 180°, what is the theorem?

Answer 12

If a quad is cyclic, then the opposite interior angles are supplementary.

Question 13

If ABCD is a cyclic quad, what is the theorem? (Hint: it’s not the same as card 8)

Answer 13

If the opposite interior angles of a quad are supplementary, then the quad is cyclic.

Question 14

If DCE = A, what is the theorem?

Answer 14

If the quad is cyclic, then the exterior angle is equal to the interior opposite.

Question 15

If ABCD is a cyclic quad, what is a third theorem?

Answer 15

If the exterior angle of a quad is equal to the interior opposite, then the quad is cyclic.

Question 16

If ABCD is a cyclic quad, what is a third theorem?

Answer 16

If the exterior angle of a quad is equal to the interior opposite, then the quad is cyclic.