circle geo theorems Flashcards
stand on chord
angles standing on the same chord are equal
lines bisecting chords
lines bisecting chords will intersect at the centre of the circle
opposite quadrilateral
opposite angles in a cyclic quadrilateral are equal
angle semi
angles in a semi circle are always 90 degrees
chords equal
- chords of equal length in a circle subtend equal angles at the centre
- chords of equal length in a circle are equidistant from the centre
perpendicular chord
The perpendicular from the centre bisects the chord
perpendicular intersect
the perpendicular bisectors of every chord of a circle intersect at the centre of the circle
product intercept
The products of the intercepts of two intersecting chords are equal
products secant
The products of the intercepts of two intersecting secants to a circle from an external point are equal
square tangent
The square of a tangent to a circle from an external point equals the product of the intercepts of any secants from the point
circles touch
when two circles touch their centres and the point of contact are collinear
tangents same point
two tangents drawn from an external point are equal in length
angle between tangent and chord
angle between tangent and a chord drawn to the point of contact is equal to the angle at the circumference in the alternate segment.It is called the alternate segment theorem.
radius tangent
The radius at the point of contact with a tangent is 90 degrees
how to answer circle geo questions
- always draw diagram if not given
- if adding extra letters introduce them by saying let m be midpoint of… or let x be the angle aod
- Make sure you answered the question , reasoning for every line, don’t skip steps, have a concluding statement for the end of your answer eg therefore ap=mb or mf perpendicular bc as required
