14626222
Description
Mind Map by Yomith Piyasiri, updated more than 1 year ago
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Created by Yomith Piyasiri
over 5 years ago
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Circle Geometry
- Angles
- Equal angles at the
centre of the circle
stand on equal arc.
- Don't need to prove
- IMPORTANT TO REMEMBER
- Equal angles at the
centre of the circle
stand on equal arc.
- Theorem- The angle at
the centre of a circle is
twice the angle at the
circumference subtended
by the same arc.
- Don't need to prove
- IMPORTANT TO REMEMBER
- Theorem- The angle at
the centre of a circle is
twice the angle at the
circumference subtended
by the same arc.
- Theorem- The angle in a
semicircle is a right angle.
- IMPORTANT TO REMEMBER
- Need to prove
- Theorem- The angle in a
semicircle is a right angle.
- Need to prove
- IMPORTANT TO REMEMBER
- shorter as, Angles
in the same
segment are equal.
- Need to prove
- Chords
- Need to
prove
- Theorem- The
perpendicular
bisector of a chord
passes through
the centre of the
circle.
- Need to
prove
- need to
prove
- Theorem 1- The
perpendicular from the
centre of a circle to a
chord bisects the chord.
- Theorem 2- The line from
the centre of a circle to
the midpoint of a chord is
perpendicular to the chord.
- Need to prove
- need to
prove
- Need to
prove
- Theorem- Chords that are
equidistant from the centre of
the circle are equal.
- with this question i saw the conce
- with this question i saw the conce
- Need to
prove
- Cyclic Quadrilaterals
- Theorem- The
opposite angles
of a cyclic
quadrilateral are
supplementary.
- Need to prove
- IMPORTANT TO REMEMBER
- Theorem- The
opposite angles
of a cyclic
quadrilateral are
supplementary.
- Theorem- An
exterior angle of a
cyclic quadrilateral is
equal to the interior
opposite angle.
- Need to
prove
- Theorem- An
exterior angle of a
cyclic quadrilateral is
equal to the interior
opposite angle.
- Theorem- If the opposite
angles in a quadrilateral are
supplementary then the
quadrilateral is cyclic.
- This is also a test
for four points to
be concyclic.
- Need to
prove
- Theorem- If the opposite
angles in a quadrilateral are
supplementary then the
quadrilateral is cyclic.
- Theorem- If two points lie on
the same side of an interval,
and the angles subtended at
these points by the interval
are equal, then the two
points and the endpoints of
the interval are concyclic.
- Need to
prove
- Theorem- If two points lie on
the same side of an interval,
and the angles subtended at
these points by the interval
are equal, then the two
points and the endpoints of
the interval are concyclic.
- Theorem- Any three
non-collinear points lie on
a unique circle, whose
centre is the point of
concurrency of the
perpendicular bisectors of
the intervals joining the
points.
- Need
to prove
- Theorem- Any three
non-collinear points lie on
a unique circle, whose
centre is the point of
concurrency of the
perpendicular bisectors of
the intervals joining the
points.
- Tangents
- Theorem- Two
circles touch if
they have a
common tangent
at the point of
contact.
- Need to prove
- Theorem- The tangent to a
circle is perpendicular to the
radius drawn to the point of
contact.
- Don't need
to prove
- Theorem- The tangent to a
circle is perpendicular to the
radius drawn to the point of
contact.
- Theorem- Tangents to a
circle from an external
point are equal.
- Need to
prove
- Looks like
Birds beak
- Need to prove
- Theorem- Tangents to a
circle from an external
point are equal.
- Don't need
to prove
- Theorem- When two
circles touch, their
centres and the point
of contact are collinear.
- Don't need
to prove
- Theorem- Angle in the alternate segment.
- The sail boat
- Need to
prove
- MOST IMPORTANT
- Theorem- Angle in the alternate segment.
- Intersecting Secants
and Chords
- Theorem- The square of
the length of the tangent
from an external point is
equal to the product of the
intercepts of the secant
passing through this point.
- Need to
prove
- Theorem- The square of
the length of the tangent
from an external point is
equal to the product of the
intercepts of the secant
passing through this point.
- Need to
prove
- Theorem- The products
of the intercepts of two
intersecting secants to a
circle from an external
point are equal.
- Need to
prove
- Need to
prove
- Theorem- The
products of the
intercepts of two
intersecting chords
are equal.
- Need to
prove
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