Circular Measure

Question 1

Answer 1

Question 2

Answer 2

Question 3

Answer 3

Question 4

Answer 4

Question 5

Theorem of Thales

Answer 5

Theorem of Thales: If AB is a diametre of a circle and P is a point on its circumference (except for A and B), then <APB=90°.

Question 6

Tangent to radius theorem

Answer 6

The tangent to a circle is perpendicular to the radius drawn to the point of tangency.

Question 7

Two tangents to radii theorem

Answer 7

From a point outside of a circle, two tangents can be drawn to the circle. The distances between the point and the two points of tangency are equal.

Question 8

Angle at the centre to angle at the circumference
Case 1: Both legs of the angle at the centre are inside the angle at the circumference

Answer 8

An angle at the centre of a circle is twice an angle at the circumference subtended by the same arc.

Question 9

Angle at the centre to angle at the circumference
Case 2: One leg of the angle at the circumference passes through the centre of the circle.

Answer 9

An angle at the centre of a circle is twice an angle at the circumference subtended by the same arc.

Question 10

Angle at the centre to angle at the circumference
Case 3: One leg of the angle at the circumference is intersecting a leg of the angle at the centre.

Answer 10

An angle at the centre of a circle is twice an angle at the circumference subtended by the same arc.

Question 11

Cyclical quadrilateral

Answer 11

If there is a circle so that each side of a quadrilateral is a chord of this circle, we call this a cyclic quadrilateral.

Question 12

Theorem of cyclic quadrilaterals

Answer 12

The opposite interior angles of a cyclic quadrilateral add up to 180 degrees.

Question 13

Intersecting Chords Theorem

Answer 13

If two chords, AB and CD, of a circle intersect at point P, then AP×PB=CP×PD.