Circle Theorems Trivia Quiz

Answer: 90 degrees

Two straight lines from either end of the diameter will always meet at a right angle to each other on the circumference. This applies regardless of the length of the diameter and circumference of the circle.

Answer: Subtended

If an angle is subtended by an arc then the point on the circumference where the straight lines from the two points meet will have a certain angle. This can be measured with a protractor. If a second example of this happens whereby from the same two points on the circumference another meeting point is formed, then that second angle will be equal to the first angle.

Angles are equal when subtended by the same arc (a=b etc).

It is also possible to say that angles are equal when subtended by the same chord. The difference between a chord and an arc is, whether a straight line is drawn between the two points marked on the circumference.

Answer: Tangent

A tangent is the name of a straight line which touches the circumference of a circle at only one point. A tangent can meet the circumference at any point around a circle.

Answer: 90 degrees

This situation also leads to the two lines, the tangent and the radius, meeting at right angles to one another. Another way to describe this would be that the tangent is perpendicular to the radius of the circle.

Answer: Double

Angles at the circumference are half the size of the angle formed at the circle's centre when the angles are created from the same two points on the circumference.

If the angle at the centre is (x) and the angle at the circumference is (y) then the equation for this rule would be - x=2y.

Answer: They total 180 degrees

Opposite angles within a cyclic quadrilateral will always total 180 degrees. In total, angles in a quadrilateral tally to make 360 degrees. That is the proof of the rule. As there are always two sets of opposing angles in a quadrilateral, each must total 180 degrees and subsequently reach the full 360 degrees.

Answer: They are equal in length

When this phenomenon occurs, the length of the two straight lines from the point of origin to the points on the circumference of the circle that they touch will be equidistant.

Answer: Both of these

The use of isosceles triangles when attempting to ascertain angles within a circle makes the process a whole lot easier. When one of the triangle's corners is situated directly on the circle's geometric centre, it is possible to know that two sides (the radii of the circle) will be equidistant. An isosceles triangle is indicated by a dash drawn over each of the two equal sides. Once the isosceles triangle is known, the missing angle can be established.

As the angle between the point at where the two equidistant lines meet is always the different sized angle, you know that the other two angles will be equal. If angle x = 50 degrees, angle y = 50 degrees. That will leave a final angle of 80 degrees, as angles in a triangle always amount to 180 degrees.

Answer: Segment

The alternate segment theory proposes that two angles in a certain structure will be equal to each other. Take angles (x) and (y). Angle (x) is situated between a chord (a line connecting two points of an arc) and a tangent. Angle (y) is situated between the meeting points of two straight lines which have been drawn from either end of the chord. This meeting point is on the circumference.

When angles (x) and (y) are found in this setup they are equal in size. The equation would be x=y.

Answer: pi x r x r x (A/360)

pi x r x r x (A/360), is much easier to say than it is to write down (pi times r squared times A divided by 360).

Pi is the number which indicates the ratio between the length of the diameter and the length of the circumference. The reason that the angle (A) is divided by the number 360 is because there are 360 degrees in a full circle.