Circle Geometry
Conjecture: a mathematical statement that
appears likely to be true, based on
your observations, but has not been
proven
Conjectures about ARCs & ANGLES…
3. The measure of a central angle equals the
measure of its corresponding minor arc
Conjectures about ARCs & ANGLES…
4. The measure of a central angle is 360o
minus the measure of the major arc with
the same endpoints as the central angle
Conjectures about ARCs & ANGLES…
5. The measure of an inscribed angle in a
circle equals half of the measurement of the
arc it intercepts (or the central angle)
central
angle
inscribed angle
Conjectures about ARCs & ANGLES…
6. All inscribed angles that intercept the same
arc will have the same measurement
arc CB
Conjectures about ARCs & ANGLES…
7. If an inscribed angle intercepts a semicircle,
then it has a measure of 90o
Conjectures about CHORDS…
1. The
perpendicular
bisector of a
chord will pass
through the centre
of the circle
Conjectures about CHORDS…
2. Congruent chords
in a circle are equal
distance from the
center of the circle
Conjectures about TANGENTS…
8. When a tangent
line and a radius
intersect at the
point of tangency,
the two lines will be
perpendicular
point of
tangency
radius
tangent line
Conjectures about TANGENTS…
9. If two tangent segments intersect outside
a circle, then the tangent segments have equal
measures