Mathematics — first biennium · Lesson
A perpendicular from the centre to a chord bisects it. In the same circle, equal chords determine equal arcs and conversely.
Prerequisites: Circle geometry and Pythagoras
Goal: Use the perpendicular from the centre to a chord and relate equal chords to equal arcs.
In this lesson: Use the perpendicular from the centre to a chord and relate equal chords to equal arcs.
New concept: A chord joins two points on a circle; an arc is the part of the circumference between those points. Equal chords subtend equal arcs and equal central angles, and conversely.
How to proceed: Radius OA is the hypotenuse of right triangle OMA. After Pythagoras remember that M is the midpoint of the chord.
You can already assume: Circle geometry and Pythagoras.
A perpendicular from the centre bisects a chord; equal chords determine equal arcs.
Completed exercises: 0/5 · Correct on first attempt: 0
Radius OA is the hypotenuse of right triangle OMA. After Pythagoras remember that M is the midpoint of the chord.
Data / situation: OA=17, OM=8 and OM⊥AB. Find chord AB.
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