How to do quick user assign in kanban in Odoo 17 ERP
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Know all about a circle
1. Know all about a Circle
THE COLLECTION OF ALL THE POINTS IN A
PLANE , WHICH ARE AT A FIXED DISTANCE
FROM A FIXED POINT IN A PLANE, IS
CALLED A CIRCLE
3. Line OB and OA are the
radii of the circle D
AB and CD are chords
of the circle
CF is also the chord of
the cirle known as C O F
DIAMETER
Diameter is the longest -
A B
---------------- of the
circle
4. Area in green part is
known as major sector
Area in minor part is
known as -----------------
And the arc comprised
in these sectors are
respectively known as
Major arc
Minor arc.
5. Angle ABC is subtended
angle in circle with
centre o
Angle DOE is the central
angle as it is making
angle at the centre.
Angles made in circle : the angles
lying anywhere ON the the circle
made by chords is known as
SUBTENDED angle ( line AC is the
chord)
6. A segment is any region
in a circle separated by a
chord
Portion in green region
is known as the Major
segment
Portion in purple color is
known as minor
segment
What is the segment
separated by a diameter Major segment , minor segment and
known as?? Semicircles
7. Quick recap of A
all the terms
From the figure aside
name the following :
1. Points in the interior of
the circle
2. Diameter of the circle O
B
3.Radius of the circle
4.Subtended angle in the
circle
5.Central angle in the
circle
C
6.Major sector
D
7.Minor sector
8.Semicricle
9. Given: Chord AB = chord DC
To Prove:
A D
angle AOB= angle DOC
Proof:
In Triangle ABC and triangle
DOC OO
AB=DC given
AO=OC radii of same circle
BO=OD radii of same circle C
B
Triangle AOB= Triangle DOC
angle AOB= angle DOC
(C.P.C.T)
Equal chords of a circle subtend
Hence proved……. equal angles at the centre
10. Given :
Angle AOB= angle COD
To prove:
A B
chord AB= Chord CD
`
Proof:
In triangle AOB and triangle
COD
C
Angle AOB= angle COD (given ) O
AO=OC radii of same circle
BO=OD radii of same circle
Triangle AOB= Triangle
DOC
D
chord AB= Chord CD
If the angles subtended by the
chords of a circle at the centre are
congruent , then the chords are
congruent.
11. Given :
OD perpendicular AB
To prove:AD=DB
Proof:
In triangle AOD and
triangle DOB O
OA=OB radius
OD=OD common side
Angle ODA=angle ODB
A D B
(90 degrees.)
Triangle AOD=ODB
(R-H-S test)
The perpendicular from the centre
of the circle bisects the chord.
AD=DB ( C.P.C.T)
12. Given : AD=DB
To prove: OD
perpendicular AB
Proof:
In triangle AOD and
triangle DOB
O
OA=OB radius
OD=OD common side
AD=DB given
triangle AOD = triangle A
DOB S-S-S test D B
Angle ODB=OAD
(C.P.C.T)
Angle ODB+angle
OAD=180 linear pair The line drawn through the centre
Angle ODB= ½ angleADB of a circle to bisect the chord is
Angle ODB=90
perpendicular to the chord
13. Circle through 1,2,3, points
ď‚— On a sheet of paper try drawing circle through one
point
ď‚— Two points
ď‚— Three points
ď‚— What do you see?
14. Answers
ď‚— Many circles can be drawn from one point
ď‚— Many circles can be drawn from two points
ď‚— But one and only one circle can be drawn from three
points.
15. Try naming them and
proving it. O
OD is perpendicular to
the line
Others are all
hypotenuse
In a right angle triangle
hypotenuse is the
longest side…
D
So
…………………………………
………. The length of the perpendicular
from a point to a line is the (shortest)
distance of the line from the centre
16. Given: AB=CD
To prove: OF=OE C
Draw OF perpendicular
to OE
A O
OOO E
F
D
B
Equal chords of a circle (or
congruent circles) are equidistant
from the centre
17. Pick statements in proper order to prove the
theorem and match the reasons
ď‚— Statements ď‚— Reasons
ď‚— AF=FB ď‚— Radii of same circle
ď‚— AF=1/2AB ď‚— C.P.C.T
ď‚— CE=ED ď‚— Given
ď‚— CE=1/2CD ď‚— Radii of same circle
ď‚— CE=AF ď‚— S-S-S test
ď‚— Chord AF=chord CE ď‚— S-A-S test
ď‚— OA =OC ď‚— Each 90 degrees
ď‚— OB=OD
ď‚— In triangles AOF and OCE
ď‚— Triangles congruent by
ď‚— Angle F= Angle E
ď‚— OF=OE
18. ď‚— Chords Equidistant from the
centre of a circle are equal in
length
ď‚— (converse of the earlier theorem)
 Try proving this…………………..
ď‚— Have fun
20. M
The angels subtended by
an arc at the centre is
double the angle
subtended by it at any
point on the remaining
part of the circle
o
Angle . AMB is half of
angle AOB
Angle AOB= angle of arc
ACB A B
Angle AMB= ½ of arc
AMB C
Angles Subtended by an Arc of a
chord.
21. Angles ADB
C
ACB
AEB E
All lie in arc AMB
D
Hence all are equal to ½
arc AMB
So angle A
B
ADB =ACB=AEB=1/2 M
arc AMB
Angles in the same segment of a
circle are equal
23. Properties of ď‚— 1. the sum of either pair of
Cyclic opposite angles of a cyclic
Quadrilateral quadrilateral is 180 degrees
ď‚— If the sum of opposite angles of a
quadrilateral is 180 degrees its
cyclic quadrilateral.