# data[].attributes.body
angle  at centre is twice of angle at circumference of the circle

48/2=24

# data[].attributes.body
(angle and is subtended by arc AD)

# data[].attributes.body
AN and DN has to be tangent to the radius of the circle.

# data[].attributes.body
Angle in centre is twice of angle at circumference.

# data[].attributes.body
Arc AD have to be subtended.

# data[].attributes.body
Angle AND = 48/2
= 24
When subtended by the arc

# data[].attributes.body
angle AND is subtended by arc AD

# data[].attributes.body
the angle at the centre of the circle is twice the angle at the circumference of the circle, thus 48 divided by 2 is 24

# data[].attributes.body
angle AND is subtended by arc AD

# data[].attributes.body
old angle AND= 48/2
= 24 (subtended by arc AD)
half of angle AND= 180-90-24
= 66 (angles in a triangle)
angle AND= 66*2
= 132

# data[].attributes.body
old angle AND= 48
new angle AND= 48/2
= 24
when subtended by the same arc, angle at the centre is twice of the angle on the circumference

# data[].attributes.body
angle AND is subtended by arc AD

# data[].attributes.headline
angle AND is 24 degree as the angle at the centre is twice the angle at the circumference 

# data[].attributes.subject
angle AND is 24 degree as the angle at the centre is twice the angle at the circumference 

# data[].attributes.headline
angle AND is 48 degree ( subtended by arc AD )

# data[].attributes.subject
angle AND is 48 degree ( subtended by arc AD )

# data[].attributes.body
48/2=24
180-90-24=66
66+66=132

# data[].attributes.headline
angle AND is 48 dived by two which is 24 as it is subtended by arc AD

# data[].attributes.subject
angle AND is 48 dived by two which is 24 as it is subtended by arc AD

# data[].attributes.body
this is because the angle AND is subtended by the arc AD

# data[].attributes.body
The angle at the centre of the circle is twice the angle of the circumference of the circle. Hence, we have to take 48 divide by 2.

# data[].attributes.body
Angle AND = 48/2
= 24 degrees(subtended by arc AD)
Angle AND = 180 - 90 - 24
= 66 degrees(angles in a triangle)
Therefore, Angle AND = 2 x 66
= 132 Degrees ( Tangent from an external point)

# data[].attributes.body
This is because angle AND is subtended by arc AD

# data[].attributes.body
When both angles are subtended by the same arc , angles at the center of the circle is twice the angle of the circumference of the circle.

# data[].attributes.body
Cuz angle AND is subtended by arc AD

# data[].attributes.body
same same

# data[].attributes.body
angle AND is sustended by arc AD

# data[].attributes.body
Angle AND is subtended by arc AD

# data[].attributes.headline
angle AND = 180-90-24 (angles in a triangle)

# data[].attributes.subject
angle AND = 180-90-24 (angles in a triangle)

# data[].attributes.body
=66
hence, angle AND= 66 x 2
=132 deg

# data[].attributes.body
= 24 deg
(angle AND is subtended by arc AD)

# data[].attributes.body
Angle AND is subtended by arc AD

# data[].attributes.body
Angle AND = 24 degree (since it is subtended by arc AC)
180-90-24=66 (Angles in a triangle)
Therefore, Angle AND = 66 multiply 2= 132

# data[].attributes.body
Angle AND = 48 degree divide by 2
= 24 (since it is subtended by arc AD

# data[].attributes.body
Angle AND is subtended by arc AD.

# data[].attributes.body
Angle AND =24 degree (subtended by arc AD)
180-90-24=66 (angles in a triangle)
Angle AND = 66 x 2
= 132 degree

# data[].attributes.body
angle AND is subtended by arc AD

# data[].attributes.body
Angle AND =48/2
=24( subtended by arc AD)

# data[].attributes.body
Angle AND is subtended by arc AD

# data[].attributes.body
angle AND = 48/2 =24
(subtended by arc AD )

# data[].attributes.body
angle AND is subtended by arc AD

# data[].attributes.headline
Angle AND = 132 degrees180 - 90 - 24 = 66 degrees (angles in a triangle)Angle AND = 66 x 2 = 132 deg (Tangents from an external point)

# data[].attributes.subject
Angle AND = 132 degrees180 - 90 - 24 = 66 degrees (angles in a triangle)Angle AND = 66 x 2 = 132 deg (Tangents from an external point)

# data[].attributes.headline
angle AND = 24 degreesangle AND = 48/2                                      =24 Deg    (subtended by arc AD)

# data[].attributes.subject
angle AND = 24 degreesangle AND = 48/2                                      =24 Deg    (subtended by arc AD)

# data[].attributes.headline
angle AND = 48 degreesangle AND is subtended by arc AD

# data[].attributes.subject
angle AND = 48 degreesangle AND is subtended by arc AD

# data[].attributes.body
angle AND = 48/2 =24
(subtended by arc AD)

# data[].attributes.body
angle AND is subtended by arc AD

# data[].attributes.body
angle AND = 48/2
= 24 degrees
(subtended by arc AD)
180 - 90 - 24 = 66 degrees
(angles in a triangle)
angle AND = 66 x 2
= 132 degrees
(tangents from an external point

# data[].attributes.body
angle AND = 48/2
= 24
angle at the centre = 2 angle at circumference subtended by the same arc.

# data[].attributes.body
angle AND is subtended by arc AD

# data[].attributes.body
Angle AND subtended by arc AD

# data[].attributes.body
The angle is subtended by Arc AD

# data[].attributes.body
Angle AND = 48/2
= 24 degrees (subtended by arc AD)
180 - 90 - 24 = 66 degrees
Angle AND = 66 x 2
= 132 degrees (tangents from an external point)

# data[].attributes.body
Angle AND = 48/2
= 24 degrees (subtended by arc AD)

# data[].attributes.body
Angle AND is subtended by Arc AD

# data[].attributes.body
The angle is subtended by Arc AD

# data[].attributes.body
48/2 = 24 degrees (subtended by arc AD)
180 - 90 - 24 = 66 degrees (angles in a triangle)
Angle AND = 66 x 2 = 132degrees (Tangents from an external point)

# data[].attributes.body
The condition include, when subtended by the same arc, angle at the centre of the circle is twice the angle of the circumference of the circle. Therefore, to get the answer, we have to divide 48 by 2 to get 24 degrees.

# data[].attributes.body
The angle is subtended by Arc AD

# data[].attributes.body
The angle is subtended by the arc AD

# data[].attributes.body
The angle is subtended by Arc AD

# data[].attributes.body
Angle AND is subtended by the major segment while angle AOD is subtended by the minor arc. As a result, angle AND + angle AOD = 180 degrees. Since angle AOD = 48 degrees, angle AND = 180 - 48 = 132 degrees.

# data[].attributes.body
If point N is on the circumference of the circle, the angle at the centre of the circle, angle AOD, is twice of the angle at the circumference, angle AND. As a result, angle AND = 48/2 = 24 degrees

# data[].attributes.body
If point N is inside the circle, angle AND will be subtended with the same arc as angle AOD, which is AD. As angle in the same segment are equal, angle AND = angle AOD = 48 degrees.

# data[].attributes.body
Having used the property (Tangents from an external point), we can calculate angle atO to be = 2(180-90-24)

# data[].attributes.body
For point N to be on the circumference of the circle, the property (When subtended by the same arc, angle at the centre is twice angle on the circumference)

# data[].attributes.body
The angle is subtended by Arc AD

# data[].attributes.body
If Angle AND were to be at the circumference, it is 24 deg. And the further the angle is from same arc AD, the smaller the angle AND. Thus, Angle AND is less than 24 deg.

# data[].attributes.body
For point N to be on the circumference of the circle, we use the property, (angle at center = 2 angle at circumference), to solve. Since O, the center, makes angle AOD is 48 deg, the angle subtended by the same arc but with point N on the circumference, makes it half of 48 deg. Therefore, angle AND is 48 deg divided by 2 to get 24 deg, which is angle AND.

# data[].attributes.body
For point N to be inside the circle and form the angle AND, it has to be subtended by the minor arc AD so as to become 48 deg. Using angles subtended by the same arc.

# data[].attributes.body
48/2=24 degrees
180-24-90=66 degrees (angles in a triangle)
Angle AND 2(66)=132 degrees

# data[].attributes.body
Angle AND 48/2=24
When both angles are subtended  by the same Arc, the angle at the centre would be twice as big as the angle at the circumference. As a result, the angle at the circumference would by 24 degrees.

# data[].attributes.body
The angle is subtended  by the minor Arc AD

# data[].attributes.body
angle OAN = angle ODN= 90 deg (tangent perpendicular to radius)
angle AND =  2(180-90-48/2)
=132 deg

# data[].attributes.body
when both angles are subtended by the same arc, the angle at the centre is twice the angle at the circumference

# data[].attributes.body
the angle is subtended by the arc, AD

# data[].attributes.body
180 deg - 24 deg - 90 deg = 66 deg
(angles in a triangle)
angle AND = 66 deg x 2 = 132 deg

# data[].attributes.headline
angle AND = 48/2 = 24 degangle at the centre = 2 times the angle at circumference subtended by the same arc

# data[].attributes.subject
angle AND = 48/2 = 24 degangle at the centre = 2 times the angle at circumference subtended by the same arc

# data[].attributes.body
as angle is subtended by the arc AD

# data[].attributes.headline
angle AND = 48 degAs angle is subtended by the arc AD

# data[].attributes.subject
angle AND = 48 degAs angle is subtended by the arc AD

# data[].attributes.body
The angle is subtended by the arc AD

# data[].attributes.body
angle AND = 48/2
= 24
angle at the center = 2 angle at circumference subtended by the same arc

# data[].attributes.body
angle AND = 48 deg
the angle is subtended by arc AD

# data[].attributes.body
Angle AND =48/2
=24 deg
An angle at the centre is twice the value of an angle at the circumference substended by the same arc

# data[].attributes.body
Angle  AND = 48 deg
the angle is substended by a common arc

# data[].attributes.body
48 deg / 2 = 24 deg
180 deg - 90 deg - 24 deg = 66 deg (angles in a triangle)
Angle AND = 66 deg x 2
= 132 deg

# data[].attributes.body
Angle AND = 48 deg / 2
= 24 degrees
(angle at center = 2 angle at circumference)

# data[].attributes.body
Angle AND = 48 deg
The angle is subtended by the minor arc AD

# data[].attributes.body
180 deg. - 24 deg. - 90 deg.
= 66 deg. (angles in a triangle)
angle AND = 66 deg x 2
= 132 deg.

# data[].attributes.body
Angle AND = 48 deg./2
= 24 deg.
An angle at the centre is twice the angle at the circumference subtended by the same arc.

# data[].attributes.body
Angle AND = 48 deg.
The angle is subtended by arcs.

# data[].attributes.body
180 degrees-24 degrees-90 degrees= 66 degrees(angles in a triangle)
angle AND= 66 x 2
= 132 degrees

# data[].attributes.headline
The angle must be subtended by arc AD. Angle = 48/2

# data[].attributes.subject
The angle must be subtended by arc AD. Angle = 48/2

# data[].attributes.body
=24 degrees

# data[].attributes.headline
The angle must be subtended by the arcs. angle=48 degrees

# data[].attributes.subject
The angle must be subtended by the arcs. angle=48 degrees

# data[].attributes.body
= 24 deg
an angle at the centre is twice an angle at the circumference subtended by the same arc

# data[].attributes.body
the angle is subtended by arcs

# data[].attributes.headline
Since N is on the same side of AD, the angle N would be on the circumference near to AD.

# data[].attributes.subject
Since N is on the same side of AD, the angle N would be on the circumference near to AD.

# data[].attributes.body
180 deg - 48 deg = 156 deg (angles at the centre and circumference, angles in a semi-circle