Circle theorems Flashcards
The angle which an arc of a circle subtends at the centre…
The angle which an arc of a circle subtends at the centre of a circle is twice the angle it subtends at any point on the remaining part of the circumference
Angles at the circumference in the same segment of a circle…
Angles at the circumference in the same segment of a circle and subtended by the same arc/chord are equal
The angle at the circumference subtended by the
The angle at the circumference subtended by the diameter is a right angle.
The opposite angles of a cyclic quadrilateral…
The opposite angles of a cyclic quadrilateral are supplementary.
The exterior angle of a cyclic quadrilateral….
is equal to the interior opposite angle.
A tangent of a circle is perpendicular
A tangent of a circle is perpendicular to the radius/diameter of that circle at the point of contact.
The lengths of two tangents
The lengths of two tangents from an external point to the points of contact on the circle are equal.
The angle between a tangent to a circle and a chord through the point of contact…
The angle between a tangent to a circle and a chord through the point of contact is equal to the angle in the alternate segment.
The line joining the centre of a circle to the midpoint of a chord…
The line joining the centre of a circle to the midpoint of a chord is perpendicular to the chord.
Conversely, a perpendicular line drawn from the centre of a circle to a chord bisects the chord.
Chord
A straight line that touches any two points on the circumference of a circle.
Diameter
A chord that passes through the centre of the circle.
Arcs
A part of the circumference of a circle that is cut off by a chord.
Segment
The region enclosed between a chord and an arc.
Sector
The region enclosed by any two radii and an arc.
Tangent
A straight line that intersects a circle at only one point. The line ‘touches’ the circumference of the circle at only one point.
