CIRCLE GEOMETRY: CATEGORY 1
Center-to-Chord Theorems (1A & 1B)
Theorem 1A: The Perpendicular Bisector
Statement: The line drawn from the center of a circle perpendicular to a chord
bisects the chord.
Exam Reason: line from centre ⊥ to chord
What does this actually mean?
If you see a line coming from the center O and it hits a chord at a 90° angle,
you can immediately assume that the line has cut the chord exactly in half.
You don't need to prove it; the 90° square is your "permission slip" to mark
both sides as equal.
Diagram for 1A
O
M
The 90° angle forces the
blue segments to be equal.
Center-to-Chord Theorems (1A & 1B)
Theorem 1A: The Perpendicular Bisector
Statement: The line drawn from the center of a circle perpendicular to a chord
bisects the chord.
Exam Reason: line from centre ⊥ to chord
What does this actually mean?
If you see a line coming from the center O and it hits a chord at a 90° angle,
you can immediately assume that the line has cut the chord exactly in half.
You don't need to prove it; the 90° square is your "permission slip" to mark
both sides as equal.
Diagram for 1A
O
M
The 90° angle forces the
blue segments to be equal.
