Proofs - Circle Theorems Flashcards
(18 cards)
State Central Angle Theorem
The angle at the centre of a circle is twice the angle at the circumference subtended by the same arc.
State Angle in a Semicircle Theorem
The angle subtended in a semicircle, or by the diameter of a circle at the circle’s circumference, is 90°
State Angle in Alternate Segment Theorem
The angle between a tangent and a chord will equal the angle subtended by the same chord at the circle’s circumference in the alternate segment.
State Lengths of Tangents Theorem
Tangents drawn from the same external point to the same circle will be equal in length.
State Intersecting Chords Theorem
PA · PB = PC · PD in the case of chords AB and CD.
Between two intersecting chords, the product of the intervals of one intersecting chord is equal to the product of the intervals of the other intersecting chord.
State Same Segment Theorem
The angle subtended by an arc at the circumference is equal to the size of another angle subtended at the circumference by the same arc.
Central Angle
An angle whose vertex is at the centre and whose sides are radii
Chord
An interval joining two points on the circle
Cyclic quadrilateral
A quadrilateral whose vertices all lie on the circumference of a circle
Diameter
A chord that passes through the centre of a circle, it also is the longest chord of a circle.
Radius
A line segment joining a point on the circle to the centre
Major/Minor Arc
A part of the circumference of the circle. A major arc represents more than half of the circumference; A minor arc represents less than half of the circumference
Major/Minor Segment
Part of a circular region enclosed between a chord (not a diameter) and the circle. A major segment encloses a region greater than that of the semicircle; a minor segment encloses a region smaller than that of the semicircle
Alternate Segment
The segment of a circle that is on the opposite side of the segment created by a chord and an arc
Major/Minor Sector
Portion of a circular region bounded by two radii and an arc. A major sector covers greater region than that of a semicircle; A minor sector covers smaller region than that of the semicircle
Secant
An extended line that cuts a circle at two distinct points
Semicircle
Half a circular region formed by the diameter and half the circle arc
Tangent
A line that contacts the circumference of a circle at one distinct point
